2 years ago · 96e1ea41e6
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				 <title>Pre-Quantum Electrodynamics</title>
			
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
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				 <!DOCTYPE html>
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</ul>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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@@ -1968,7 +1712,7 @@ Wiley, 1986 [2nd edition]
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
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@@ -1,7 +1,7 @@
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1885,7 +1629,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1891,7 +1635,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_cs.html
+++ b/build/c_m_cs.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1887,7 +1631,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_cs_cyl.html
+++ b/build/c_m_cs_cyl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details open="">
			
 
				
				-<summary class="toc-currentpage">
			
 
				
				+<li class="toc-currentpage">
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_sph_lap.html">Laplacian&emsp;<small>[c.m.cs.sph.lap]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl_grad.html">Gradient&emsp;<small>[c.m.cs.cyl.grad]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_sph.html">Spherical Coordinates&emsp;<small>[c.m.cs.sph]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_hyp.html">Hyperbolic Coordinates&emsp;<small>[c.m.cs.hyp]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_cyl" class="outline-5">
			
 
				
				 <h5 id="c_m_cs_cyl">Cylindrical Coordinates<a class="headline-permalink" href="./c_m_cs_cyl.html#c_m_cs_cyl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1928,14 +1672,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 <div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
			
 
				
				 <h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
			
 
				
				 <div class="outline-text-6" id="text-c_m_cs_cyl_grad">
			
 
				
				-<div class="eqlabel" id="org958f79a">
			
 
				
				+<div class="eqlabel" id="org1f82008">
			
 
				
				 <p>
			
 
				
				 <a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a>
			
 
				
				 </p>
			
 
				
				-<div class="alteqlabels" id="org6b4b020">
			
 
				
				+<div class="alteqlabels" id="org0d07fad">
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>Gr4(1.79)</li>
			
 
				
				 </ul>
			
@@ -1962,14 +1706,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 <div id="outline-container-c_m_cs_cyl_div" class="outline-6">
			
 
				
				 <h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
			
 
				
				 <div class="outline-text-6" id="text-c_m_cs_cyl_div">
			
 
				
				-<div class="eqlabel" id="orgb4915c4">
			
 
				
				+<div class="eqlabel" id="org9646f8e">
			
 
				
				 <p>
			
 
				
				 <a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a>
			
 
				
				 </p>
			
 
				
				-<div class="alteqlabels" id="org482df89">
			
 
				
				+<div class="alteqlabels" id="orgef4d1a0">
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>Gr4(2.21)</li>
			
 
				
				 </ul>
			
@@ -1980,10 +1724,10 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v<sub>r</sub>)
			
 
				
				+{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r} \frac{\partial}{\partial r} (r v_r)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{1}{r} \frac{∂ v<sub>φ</sub>}{∂ φ} + \frac{\partial v_z}{\partial z}.</li>
			
 
				
				+<li>\frac{1}{r} \frac{∂ v_{φ}}{∂ φ} + \frac{\partial v_z}{\partial z}.</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \tag{cyl_div}
			
@@ -1996,14 +1740,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 <div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
			
 
				
				 <h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
			
 
				
				 <div class="outline-text-6" id="text-c_m_cs_cyl_curl">
			
 
				
				-<div class="eqlabel" id="org79951eb">
			
 
				
				+<div class="eqlabel" id="org174b722">
			
 
				
				 <p>
			
 
				
				 <a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a>
			
 
				
				 </p>
			
 
				
				-<div class="alteqlabels" id="org53de84b">
			
 
				
				+<div class="alteqlabels" id="org9f83d45">
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>Gr4(2.21)</li>
			
 
				
				 </ul>
			
@@ -2014,11 +1758,11 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v<sub>φ</sub>}{∂ z}\right) ~\hat{\bf r}
			
 
				
				+{\boldsymbol ∇} × {\bf v} = \left( \frac{1}{r} \frac{\partial v_z}{\partial \phi} - \frac{∂ v_{φ}}{∂ z}\right) ~\hat{\bf r}
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>\left( \frac{\partial v_r}{\partial z} - \frac{\partial v_z}{\partial r} \right) ~\hat{\boldsymbol \phi}</li>
			
 
				
				-<li>\frac{1}{r} \left( \frac{\partial}{\partial r} (r v<sub>φ</sub>) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}</li>
			
 
				
				+<li>\frac{1}{r} \left( \frac{\partial}{\partial r} (r v_{φ}) - \frac{\partial v_r}{\partial \phi} \right) ~\hat{\bf z}</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \tag{cyl_curl}
			
@@ -2033,7 +1777,7 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 <div class="outline-text-6" id="text-c_m_cs_cyl_lap">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇}<sup>2</sup> T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
			
 
				
				+{\boldsymbol ∇}^2 T = \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>\frac{1}{r^2} \frac{\partial^2 T}{\partial \phi^2} + \frac{\partial^2 T}{\partial z^2}</li>
			
@@ -2051,7 +1795,7 @@ Range of parameters:  \(r \in [0, \infty[\), \(\phi \in [0, 2\pi[\) and \(z \in
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_cs_hyp.html
+++ b/build/c_m_cs_hyp.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-</li>
			
 
				
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				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
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				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_cyl_lap.html">Laplacian&emsp;<small>[c.m.cs.cyl.lap]</small></a></li><li>Next:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_hyp" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Next:&nbsp;<a href="c_m_dd.html">Dirac delta Distribution&emsp;<small>[c.m.dd]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_hyp" class="outline-5">
			
 
				
				 <h5 id="c_m_cs_hyp">Hyperbolic Coordinates<a class="headline-permalink" href="./c_m_cs_hyp.html#c_m_cs_hyp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
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@@ -1880,7 +1624,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_cs_sph.html
+++ b/build/c_m_cs_sph.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1702,63 +1513,13 @@ Table of contents
 
				
				 
			
 
				
				 </summary>
			
 
				
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				-<li>
			
 
				
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				-<details open="">
			
 
				
				-<summary class="toc-currentpage">
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1868,19 +1612,12 @@ Table of contents
 
				
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				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_sph_grad.html">Gradient&emsp;<small>[c.m.cs.sph.grad]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li><li>Next:&nbsp;<a href="c_m_cs_cyl.html">Cylindrical Coordinates&emsp;<small>[c.m.cs.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m_cs.html">Coordinate Systems&emsp;<small>[c.m.cs]</small></a></li></ul><div id="outline-container-c_m_cs_sph" class="outline-5">
			
 
				
				 <h5 id="c_m_cs_sph">Spherical Coordinates<a class="headline-permalink" href="./c_m_cs_sph.html#c_m_cs_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a><span class="headline-id">c.m.cs.sph</span></h5>
			
 
				
				 <div class="outline-text-5" id="text-c_m_cs_sph">
			
 
				
				-
			
 
				
				-<figure id="org7966655">
			
 
				
				-<img src="fig/sphere.png" alt="sphere" title="sphere" width="200px">
			
 
				
				-
			
 
				
				-<figcaption><span class="figure-number">Figure 1: </span>Sphere drawn with Asymptote</figcaption>
			
 
				
				-</figure>
			
 
				
				-
			
 
				
				 <p>
			
 
				
				 \((r, \theta, \phi)\).  \(\theta\) is the <b>polar angle</b>, \(\phi\) the <b>azimuthal angle</b>.
			
 
				
				 </p>
			
@@ -1970,10 +1707,10 @@ Infinitesimal surface element:  depends on situation.
 
				
				 <div class="outline-text-6" id="text-c_m_cs_sph_div">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r<sup>2</sup> v<sub>r</sub>) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v<sub>θ</sub>)
			
 
				
				+{\boldsymbol ∇} ⋅ {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (sinθ v_{θ})
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{1}{r \sin \theta} \frac{∂ v<sub>φ</sub>}{∂ φ}</li>
			
 
				
				+<li>\frac{1}{r \sin \theta} \frac{∂ v_{φ}}{∂ φ}</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \label{Gr(1.71)}
			
@@ -1987,11 +1724,11 @@ Infinitesimal surface element:  depends on situation.
 
				
				 <div class="outline-text-6" id="text-c_m_cs_sph_curl">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v<sub>φ</sub>) - \frac{∂ v<sub>θ</sub>}{∂ φ} \right] \hat{\bf r}
			
 
				
				+{\boldsymbol ∇} × {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (sin θ v_{φ}) - \frac{∂ v_{θ}}{∂ φ} \right] \hat{\bf r}
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v<sub>φ</sub>) \right] \hat{\boldsymbol \theta}</li>
			
 
				
				-<li>\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v<sub>θ</sub>) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}</li>
			
 
				
				+<li>\frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{φ}) \right] \hat{\boldsymbol \theta}</li>
			
 
				
				+<li>\frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{θ}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \label{Gr(1.72)}
			
@@ -2005,7 +1742,7 @@ Infinitesimal surface element:  depends on situation.
 
				
				 <div class="outline-text-6" id="text-c_m_cs_sph_lap">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇}<sup>2</sup> T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r<sup>2</sup> \frac{\partial T}{\partial r}\right)
			
 
				
				+{\boldsymbol ∇}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>\frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( sin θ \frac{\partial T}{\partial \theta}\right)</li>
			
@@ -2024,7 +1761,7 @@ Infinitesimal surface element:  depends on situation.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc.html
+++ b/build/c_m_dc.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1890,7 +1634,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_curl.html
+++ b/build/c_m_dc_curl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1892,7 +1636,7 @@ v_x &amp; v_y &amp; v_z \end{array} \right| \nonumber \\
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_d2.html
+++ b/build/c_m_dc_d2.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1598,38 +1459,9 @@ Table of contents
 
				
				 <a href="./c_m_dc_pr.html#c_m_dc_pr">Product Rules</a><span class="headline-id">c.m.dc.pr</span>
			
 
				
				 
			
 
				
				 </li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details open="">
			
 
				
				-<summary class="toc-currentpage">
			
 
				
				+<li class="toc-currentpage">
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Next:&nbsp;<a href="orge025182.html">Divergence of gradient&emsp;<small>[orge025182]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Next:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul><div id="outline-container-c_m_dc_d2" class="outline-5">
			
 
				
				 <h5 id="c_m_dc_d2">Second Derivatives<a class="headline-permalink" href="./c_m_dc_d2.html#c_m_dc_d2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1876,9 +1620,9 @@ Table of contents
 
				
				 <div class="outline-text-5" id="text-c_m_dc_d2">
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-orge025182" class="outline-6">
			
 
				
				-<h6 id="orge025182"><a href="#orge025182">Divergence of gradient</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-orge025182">
			
 
				
				+<div id="outline-container-orgc3b89bb" class="outline-6">
			
 
				
				+<h6 id="orgc3b89bb"><a href="#orgc3b89bb">Divergence of gradient</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-orgc3b89bb">
			
 
				
				 <p>
			
 
				
				 \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
			
 
				
				 The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
			
@@ -1887,36 +1631,36 @@ given by the Laplacian of the corresponding vector elements.
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-orgacb930d" class="outline-6">
			
 
				
				-<h6 id="orgacb930d"><a href="#orgacb930d">Curl of a gradient</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-orgacb930d">
			
 
				
				+<div id="outline-container-org5caf3f5" class="outline-6">
			
 
				
				+<h6 id="org5caf3f5"><a href="#org5caf3f5">Curl of a gradient</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-org5caf3f5">
			
 
				
				 <p>
			
 
				
				 This always vanishes.
			
 
				
				 </p>
			
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-org6caee98" class="outline-6">
			
 
				
				-<h6 id="org6caee98"><a href="#org6caee98">Gradient of the divergence</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-org6caee98">
			
 
				
				+<div id="outline-container-org4f9116a" class="outline-6">
			
 
				
				+<h6 id="org4f9116a"><a href="#org4f9116a">Gradient of the divergence</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-org4f9116a">
			
 
				
				 <p>
			
 
				
				 \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics.  No special name.
			
 
				
				 </p>
			
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-orgb5da747" class="outline-6">
			
 
				
				-<h6 id="orgb5da747"><a href="#orgb5da747">Divergence of a curl</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-orgb5da747">
			
 
				
				+<div id="outline-container-org2c1c081" class="outline-6">
			
 
				
				+<h6 id="org2c1c081"><a href="#org2c1c081">Divergence of a curl</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-org2c1c081">
			
 
				
				 <p>
			
 
				
				 This always vanishes.
			
 
				
				 </p>
			
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-orgebcbadc" class="outline-6">
			
 
				
				-<h6 id="orgebcbadc"><a href="#orgebcbadc">Curl of curl</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-orgebcbadc">
			
 
				
				+<div id="outline-container-orgc977e97" class="outline-6">
			
 
				
				+<h6 id="orgc977e97"><a href="#orgc977e97">Curl of curl</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-orgc977e97">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 {\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
			
@@ -1930,7 +1674,7 @@ This always vanishes.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_del.html
+++ b/build/c_m_dc_del.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1891,7 +1635,7 @@ The <b>del/grad/nabla operator</b> is defined as
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_div.html
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@@ -1,7 +1,7 @@
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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@@ -565,29 +502,8 @@ Table of contents
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1888,7 +1632,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_g.html
+++ b/build/c_m_dc_g.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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				 </summary>
			
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1912,7 +1656,7 @@ is a vector called the <b>gradient</b> of \(T\).
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dc_pr.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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@@ -1885,7 +1629,7 @@ Six product rules (on inside front cover of Gr).
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dd.html
+++ b/build/c_m_dd.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1887,7 +1631,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dd_1d.html
+++ b/build/c_m_dd_1d.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1899,7 +1643,7 @@ Consequences:  for any smooth differentiable function \(f(x)\),
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dd_3d.html
+++ b/build/c_m_dd_3d.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1903,11 +1647,27 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
 
				
				 More generally,
			
 
				
				 </p>
			
 
				
				 
			
 
				
				+<div class="eqlabel" id="org99c1900">
			
 
				
				+<p>
			
 
				
				+<a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				+  <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				+  <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				+</svg></a>
			
 
				
				+</p>
			
 
				
				+<div class="alteqlabels" id="orge7a14d6">
			
 
				
				+<ul class="org-ul">
			
 
				
				+<li>Gr (1.100)</li>
			
 
				
				+</ul>
			
 
				
				+
			
 
				
				+</div>
			
 
				
				+
			
 
				
				+</div>
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 \boxed{
			
 
				
				 {\boldsymbol \nabla} \cdot \left(\frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3} \right)= 4\pi \delta^{(3)} ({\bf r}).
			
 
				
				-}\label{Gr(1.100)}
			
 
				
				+}
			
 
				
				+\tag{divdel}\label{divdel}
			
 
				
				 \]
			
 
				
				 </p>
			
 
				
				 
			
@@ -1938,7 +1698,7 @@ we have that
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_dd_div.html
+++ b/build/c_m_dd_div.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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@@ -1909,7 +1653,7 @@ Problem:  in (1.84), we've divided by zero when \(r = 0\).
 
				
				 
			
 
				
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				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="orgebcbadc.html">Curl of curl&emsp;<small>[orgebcbadc]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_d2.html">Second Derivatives&emsp;<small>[c.m.dc.d2]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
			
 
				
				 <h4 id="c_m_ic">Integral Calculus<a class="headline-permalink" href="./c_m_ic.html#c_m_ic"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
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@@ -1890,7 +1634,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_ftc.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="org5c24b4a.html">Volume Integrals&emsp;<small>[org5c24b4a]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic_lsv.html">Line, Surface and Volume Integrals&emsp;<small>[c.m.ic.lsv]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftg.html">The Fundamental Theorem for Gradients&emsp;<small>[c.m.ic.ftg]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_ftc" class="outline-5">
			
 
				
				 <h5 id="c_m_ic_ftc">The Fundamental Theorem of Calculus<a class="headline-permalink" href="./c_m_ic_ftc.html#c_m_ic_ftc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
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				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1888,7 +1632,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_ftg.html
+++ b/build/c_m_ic_ftg.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1897,7 +1641,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_gauss.html
+++ b/build/c_m_ic_gauss.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1891,7 +1635,7 @@ This is know either as <b>Gauss' theorem</b>, <b>Green's theorem</b> or the <b>d
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_ip.html
+++ b/build/c_m_ic_ip.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1878,39 +1622,27 @@ Table of contents
 
				
				 Example:  \({\boldsymbol \nabla} \cdot (f{\bf A}) = f({\boldsymbol \nabla} \cdot {\bf A}) + {\bf A} \cdot ({\boldsymbol \nabla} f)\) implies (via Gauss' theorem)
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<p>
			
 
				
				-\[
			
 
				
				-∫<sub>\cal V</sub> {\boldsymbol ∇} ⋅ (f{\bf A}) dτ = ∫<sub>\cal V</sub> f({\boldsymbol ∇} ⋅ {\bf A}) dτ
			
 
				
				-</p>
			
 
				
				-<ul class="org-ul">
			
 
				
				-<li>∫<sub>\cal V</sub> {\bf A} ⋅ ({\boldsymbol ∇} f) dτ = \oint f{\bf A} ⋅ d{\bf a},</li>
			
 
				
				-</ul>
			
 
				
				-<p>
			
 
				
				-\]
			
 
				
				-</p>
			
 
				
				+\begin{equation*}
			
 
				
				+\int_{\cal V} {\boldsymbol \nabla} \cdot (f{\bf A}) d\tau = \int_{\cal V} f({\boldsymbol \nabla} \cdot {\bf A}) d\tau
			
 
				
				++ \int_{\cal V} {\bf A} \cdot ({\boldsymbol \nabla} f) d\tau = \oint f{\bf A} \cdot d{\bf a},
			
 
				
				+\end{equation*}
			
 
				
				 
			
 
				
				 <p>
			
 
				
				 or in other words
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<p>
			
 
				
				-\[
			
 
				
				-∫<sub>\cal V</sub> f({\boldsymbol ∇} ⋅ {\bf A}) dτ = -∫<sub>\cal V</sub> {\bf A} ⋅ ({\boldsymbol ∇} f) dτ
			
 
				
				-</p>
			
 
				
				-<ul class="org-ul">
			
 
				
				-<li>\oint<sub>\cal S</sub> f{\bf A} ⋅ d{\bf a}.</li>
			
 
				
				-</ul>
			
 
				
				-<p>
			
 
				
				+\begin{equation}
			
 
				
				+\int_{\cal V} f({\boldsymbol \nabla} \cdot {\bf A}) d\tau = -\int_{\cal V} {\bf A} \cdot ({\boldsymbol \nabla} f) d\tau
			
 
				
				++ \oint_{\cal S} f{\bf A} \cdot d{\bf a}.
			
 
				
				 \label{Gr(1.59)}
			
 
				
				-\]
			
 
				
				-</p>
			
 
				
				+\end{equation}
			
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_lsv.html
+++ b/build/c_m_ic_lsv.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1644,30 +1476,9 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
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				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="org638a76f.html">Line Integrals&emsp;<small>[org638a76f]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Next:&nbsp;<a href="c_m_ic_ftc.html">The Fundamental Theorem of Calculus&emsp;<small>[c.m.ic.ftc]</small></a></li><li>Up:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li></ul><div id="outline-container-c_m_ic_lsv" class="outline-5">
			
 
				
				 <h5 id="c_m_ic_lsv">Line, Surface and Volume Integrals<a class="headline-permalink" href="./c_m_ic_lsv.html#c_m_ic_lsv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
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				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1876,9 +1620,9 @@ Table of contents
 
				
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				-<div id="outline-container-org638a76f" class="outline-6">
			
 
				
				-<h6 id="org638a76f"><a href="#org638a76f">Line Integrals</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-org638a76f">
			
 
				
				+<div id="outline-container-org860e5de" class="outline-6">
			
 
				
				+<h6 id="org860e5de"><a href="#org860e5de">Line Integrals</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-org860e5de">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 {\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
			
@@ -1907,9 +1651,9 @@ Integral over a closed loop:
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-orgd8e925a" class="outline-6">
			
 
				
				-<h6 id="orgd8e925a"><a href="#orgd8e925a">Surface Integrals</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-orgd8e925a">
			
 
				
				+<div id="outline-container-orged48130" class="outline-6">
			
 
				
				+<h6 id="orged48130"><a href="#orged48130">Surface Integrals</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-orged48130">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 \int_{\cal S} {\bf v} \cdot d{\bf a}
			
@@ -1929,9 +1673,9 @@ Over a closed surface:
 
				
				 </div>
			
 
				
				 </div>
			
 
				
				 
			
 
				
				-<div id="outline-container-org5c24b4a" class="outline-6">
			
 
				
				-<h6 id="org5c24b4a"><a href="#org5c24b4a">Volume Integrals</a></h6>
			
 
				
				-<div class="outline-text-6" id="text-org5c24b4a">
			
 
				
				+<div id="outline-container-org4728536" class="outline-6">
			
 
				
				+<h6 id="org4728536"><a href="#org4728536">Volume Integrals</a></h6>
			
 
				
				+<div class="outline-text-6" id="text-org4728536">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 \int_{\cal V} T d\tau
			
@@ -1959,7 +1703,7 @@ d\tau = dx dy dz
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_ic_stokes.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				 </li>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
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@@ -1874,10 +1618,25 @@ Table of contents
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a><span class="headline-id">c.m.ic.stokes</span></h5>
			
 
				
				 <div class="outline-text-5" id="text-c_m_ic_stokes">
			
 
				
				+<div class="eqlabel" id="orgda53253">
			
 
				
				+<p>
			
 
				
				+<a id="Stokes"></a><a href="./c_m_ic_stokes.html#Stokes"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				+  <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				+  <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				+</svg></a>
			
 
				
				+</p>
			
 
				
				+<div class="alteqlabels" id="org14a6dc8">
			
 
				
				+<ul class="org-ul">
			
 
				
				+<li>Gr (1.57)</li>
			
 
				
				+</ul>
			
 
				
				+
			
 
				
				+</div>
			
 
				
				+
			
 
				
				+</div>
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				 \int_{\cal S} ({\boldsymbol \nabla} \times {\bf v}) \cdot d{\bf a} = \oint_{\cal P} {\bf v} \cdot d{\bf l}.
			
 
				
				-\label{Gr(1.57)}
			
 
				
				+\tag{Stokes}\label{Stokes}
			
 
				
				 \]
			
 
				
				 </p>
			
 
				
				 
			
@@ -1898,7 +1657,7 @@ the boundary shrinks to a point.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_uf.html
+++ b/build/c_m_uf.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_pot_solen.html">Theorem 2:  Divergence-less (solenoidal) fields&emsp;<small>[c.m.vf.pot.solen]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_pot.html">Potentials&emsp;<small>[c.m.vf.pot]</small></a></li><li>Next:&nbsp;<a href="c_m_uf_cyl.html">Cylindrical coordinates&emsp;<small>[c.m.uf.cyl]</small></a></li><li>Up:&nbsp;<a href="c_m.html">Mathematics&emsp;<small>[c.m]</small></a></li></ul>
			
 
				
				 <h4 id="c_m_uf">Useful Formulas<a class="headline-permalink" href="./c_m_uf.html#c_m_uf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1887,7 +1631,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_uf_cyl.html
+++ b/build/c_m_uf_cyl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1900,7 +1644,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_uf_sph.html
+++ b/build/c_m_uf_sph.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1900,7 +1644,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_uf_vi.html
+++ b/build/c_m_uf_vi.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1903,7 +1647,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va.html
+++ b/build/c_m_va.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1889,7 +1633,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va_cp.html
+++ b/build/c_m_va_cp.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1874,18 +1618,12 @@ Table of contents
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
 
				
				 </svg></a><span class="headline-id">c.m.va.cp</span></h5>
			
 
				
				 <div class="outline-text-5" id="text-c_m_va_cp">
			
 
				
				-<p>
			
 
				
				-\[
			
 
				
				-  {\bf A} × {\bf B} = \left| \begin{array}{ccc} \hat{x} &amp; \hat{y} &amp; \hat{z} <br>
			
 
				
				-    A<sub>x</sub> &amp; A<sub>y</sub> &amp; A<sub>z</sub> \\ B<sub>x</sub> &amp; B<sub>y</sub> &amp; B<sub>z</sub> \end{array} \right|
			
 
				
				-  = \left( A<sub>y</sub> B<sub>z</sub> - A<sub>z</sub> B<sub>y</sub> \right) \hat{x} + \left( B<sub>z</sub> A<sub>x</sub> - B<sub>x</sub> A<sub>z</sub> \right) \hat{y}
			
 
				
				-</p>
			
 
				
				-<ul class="org-ul">
			
 
				
				-<li>\left( A<sub>x</sub> B<sub>y</sub> - A<sub>y</sub> B<sub>x</sub> \right) \hat{z}</li>
			
 
				
				-</ul>
			
 
				
				-<p>
			
 
				
				-\]
			
 
				
				-</p>
			
 
				
				+\begin{equation*}
			
 
				
				+  {\bf A} \times {\bf B} = \left| \begin{array}{ccc} \hat{x} &amp; \hat{y} &amp; \hat{z} \\
			
 
				
				+    A_x &amp; A_y &amp; A_z \\ B_x &amp; B_y &amp; B_z \end{array} \right|
			
 
				
				+  = \left( A_y B_z - A_z B_y \right) \hat{x} + \left( B_z A_x - B_x A_z \right) \hat{y}
			
 
				
				+  + \left( A_x B_y - A_y B_x \right) \hat{z}
			
 
				
				+\end{equation*}
			
 
				
				 
			
 
				
				 <p>
			
 
				
				 The cross product is distributive:
			
@@ -1924,7 +1662,7 @@ this relation making plain that
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va_n.html
+++ b/build/c_m_va_n.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1913,7 +1657,7 @@ Component notation (in \({\mathbb R}^3\) with cartesian coordinates):
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va_pds.html
+++ b/build/c_m_va_pds.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1947,7 +1691,7 @@ Separation vector:  for two position vectors \({\bf r}_a, {\bf r}_b\),
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va_sp.html
+++ b/build/c_m_va_sp.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1913,7 +1657,7 @@ In a general coordinate system with metric \(g\),
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_va_tp.html
+++ b/build/c_m_va_tp.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1960,7 +1704,7 @@ All higher vector products can be reduced to combinations of single vector produ
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_vf.html
+++ b/build/c_m_vf.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1886,7 +1630,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_vf_helm.html
+++ b/build/c_m_vf_helm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1905,7 +1649,7 @@ where
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/c_m_vf_pot.html
+++ b/build/c_m_vf_pot.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <meta charset="utf-8">
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1806,26 +1567,9 @@ Table of contents
 
				
				 <a href="./c_m_vf_helm.html#c_m_vf_helm">The Helmholtz Theorem</a><span class="headline-id">c.m.vf.helm</span>
			
 
				
				 
			
 
				
				 </li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details open="">
			
 
				
				-<summary class="toc-currentpage">
			
 
				
				+<li class="toc-currentpage">
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_vf_pot_irrot.html">Theorem 1:  Curl-less (irrotational) fields&emsp;<small>[c.m.vf.pot.irrot]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_vf_helm.html">The Helmholtz Theorem&emsp;<small>[c.m.vf.helm]</small></a></li><li>Next:&nbsp;<a href="c_m_uf.html">Useful Formulas&emsp;<small>[c.m.uf]</small></a></li><li>Up:&nbsp;<a href="c_m_vf.html">Vector Fields&emsp;<small>[c.m.vf]</small></a></li></ul><div id="outline-container-c_m_vf_pot" class="outline-5">
			
 
				
				 <h5 id="c_m_vf_pot">Potentials<a class="headline-permalink" href="./c_m_vf_pot.html#c_m_vf_pot"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1934,7 +1678,7 @@ The following conditions are equivalent:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d.html
+++ b/build/d.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">d</span></h2>
			
 
				
				 
			
 
				
				 <div class="outline-text-2" id="text-d">
			
 
				
				-<details class="objectives" id="org9eceddd">
			
 
				
				-<summary id="org7f1879e">
			
 
				
				+<details class="objectives" id="org8e87179">
			
 
				
				+<summary id="org5aefd0c">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 
			
@@ -1927,7 +1671,7 @@ I have little doubt you'll pass the course.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emd.html
+++ b/build/d_emd.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1907,7 +1651,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emd_ce.html
+++ b/build/d_emd_ce.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1902,7 +1646,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emd_emw.html
+++ b/build/d_emd_emw.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
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@@ -1905,7 +1649,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emf.html
+++ b/build/d_emf.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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@@ -1902,7 +1646,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_ems.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <li>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1924,7 +1668,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_ems_ca.html
+++ b/build/d_ems_ca.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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@@ -1907,7 +1651,7 @@ a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conductin
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
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				 <!DOCTYPE html>
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </summary>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <li>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1904,7 +1648,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emsm.html
+++ b/build/d_emsm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1907,7 +1651,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_emsm_msm.html
+++ b/build/d_emsm_msm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1905,7 +1649,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_m.html
+++ b/build/d_m.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1915,7 +1659,7 @@ Things you should be able to do (ideally: from scratch, on a blank sheet of pape
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/d_red.html
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@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
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				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1909,7 +1653,7 @@ As a strict minimum, you should be able to:
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd.html
+++ b/build/emd.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">emd</span></h2>
			
 
				
				 
			
 
				
				 <div class="outline-text-2" id="text-emd">
			
 
				
				-<details class="prereq" id="orgbacc774">
			
 
				
				-<summary id="org2beb4f2">
			
 
				
				+<details class="prereq" id="orgfca423d">
			
 
				
				+<summary id="org226d692">
			
 
				
				 Prerequisites
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1885,8 +1629,8 @@ Prerequisites
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 
			
 
				
				-<details class="objectives" id="org53819c5">
			
 
				
				-<summary id="org725bc8f">
			
 
				
				+<details class="objectives" id="org9195c9d">
			
 
				
				+<summary id="org58d183b">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1914,7 +1658,7 @@ Objectives
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Fl.html
+++ b/build/emd_Fl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1888,7 +1632,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Fl_Fl.html
+++ b/build/emd_Fl_Fl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1915,7 +1659,7 @@ Empirically:  the changing magnetic field induces an electric current around
 
				
				 the circuit. This current is really driven by an electric field having a component
			
 
				
				 along the wire.  The line integral of this field is called the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgd356b92">
			
 
				
				+<div class="core div" id="org9907fe5">
			
 
				
				 <p>
			
 
				
				 <b>Electromotive force (or electromotance)</b>,
			
 
				
				   \[
			
@@ -1937,7 +1681,7 @@ to the rate of change of the magnetic flux,
 
				
				 \]
			
 
				
				 so we obtain
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org32cfcb5">
			
 
				
				+<div class="core div" id="org511a243">
			
 
				
				 <p>
			
 
				
				 <b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
			
 
				
				   \[
			
@@ -1955,7 +1699,7 @@ for any loop (on a wire or not). Using Stokes' theorem,
 
				
				 \]
			
 
				
				 we obtain
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org1c1c2f9">
			
 
				
				+<div class="core div" id="orgb9e0e05">
			
 
				
				 <p>
			
 
				
				 <b>Faraday's law</b> (differential form)
			
 
				
				   \[
			
@@ -1968,7 +1712,7 @@ we obtain
 
				
				 <p>
			
 
				
				 Right-hand rule always sorts signs out.  Easier rule:  {\bf Lenz's law}, which
			
 
				
				 states that {\bf nature resists a change in flux}.  This is in fact just
			
 
				
				-{\bf Le Ch\<sup>atelier</sup>'s principle} of any action at an equilibrium point leading
			
 
				
				+{\bf Le Ch\^atelier's principle} of any action at an equilibrium point leading
			
 
				
				 to an opposing counter-reaction.
			
 
				
				 </p>
			
 
				
				 </div>
			
@@ -1979,7 +1723,7 @@ to an opposing counter-reaction.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Fl_e.html
+++ b/build/emd_Fl_e.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1934,7 +1678,7 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
 
				
				 \]
			
 
				
				 We can integrate over all space:  after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orga28c6ab">
			
 
				
				+<div class="core div" id="org0a53c4e">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     W_{mag} = \frac{1}{2\mu_0} \int d\tau B^2
			
@@ -1955,7 +1699,7 @@ W_{mag} = \frac{1}{2} \int d\tau ({\bf A} \cdot {\bf J}) = \frac{1}{2\mu_0} \int
 
				
				 \hspace{2cm} \mbox{(7.31 and 7.34)}
			
 
				
				 \end{align}
			
 
				
				 
			
 
				
				-<div class="example div" id="orgda554ea">
			
 
				
				+<div class="example div" id="orge7b1ecf">
			
 
				
				 <p>
			
 
				
				 \paragraph{Example 7.13:}  coaxial cable (inner cylinder radius \(a\), outer \(b\)) carries current \(I\).
			
 
				
				 Find energy stored in section of length \(l\).
			
@@ -1981,7 +1725,7 @@ Note:  gives easy way to find inductance, since \(W = \frac{1}{2} L I^2\).
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Fl_i.html
+++ b/build/emd_Fl_i.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1914,7 +1658,7 @@ M_{12} = M_{21}
 
				
				 \]
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<div class="example div" id="orgd531765">
			
 
				
				+<div class="example div" id="orgc2d0a32">
			
 
				
				 <p>
			
 
				
				 \paragraph{Example 7.10:}
			
 
				
				 short solenoid (length \(l\), radius \(a\), \(n_1\) turns per unit length) lies concentrically inside
			
@@ -1964,7 +1708,7 @@ Inductance:  measured in {\bf henries} (\(H\)).  \(H = V s/A\).
 
				
				 </p>
			
 
				
				 
			
 
				
				 
			
 
				
				-<div class="example div" id="org702ff70">
			
 
				
				+<div class="example div" id="org7f4b3fa">
			
 
				
				 <p>
			
 
				
				 \paragraph{Example 7.11:}  find self-inductance of toroidal coil with
			
 
				
				 rectangular cross-section (inner radius \(a\), outer radius \(b\), height \(h\))
			
@@ -1991,7 +1735,7 @@ Total flux:  \(N\) times this, so self-inductance is
 
				
				 Inductance (like capacitance) is intrinsically positive.  Use Lenz law.  Think of {\bf back EMF}.
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<div class="example div" id="org6b58768">
			
 
				
				+<div class="example div" id="org37841ae">
			
 
				
				 <p>
			
 
				
				 \paragraph{Example 7.12:}  circuit with inductance \(L\), resistor \(R\) and battery \({\cal E}_0\).
			
 
				
				 What is the current ?
			
@@ -2017,7 +1761,7 @@ where \(\tau \equiv L/R\) is the {\bf time constant} of the circuit.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Fl_ief.html
+++ b/build/emd_Fl_ief.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1898,7 +1642,7 @@ law in integral form:
 
				
				 
			
 
				
				 
			
 
				
				 
			
 
				
				-<div class="example div" id="org1bfc56c">
			
 
				
				+<div class="example div" id="orgfe52c32">
			
 
				
				 <p>
			
 
				
				 {\bf Example 7.7:}
			
 
				
				 \({\bf B}(t)\) points up in circular region of radius \(R\).  What is the induced \({\bf E}(t)\) ?
			
@@ -1914,7 +1658,7 @@ Increasing \({\bf B}\):  clockwise (viewed from above) \({\bf E}\) from Lenz.
 
				
				 </div>
			
 
				
				 
			
 
				
				 
			
 
				
				-<div class="example div" id="orgd8b7646">
			
 
				
				+<div class="example div" id="orgb289794">
			
 
				
				 <p>
			
 
				
				 {\bf Example 7.8:} wheel or radius \(b\) with line charge \(\lambda\) on the rim.
			
 
				
				 Uniform magnetic field \({\bf B}_0\) in central region up to \(a &lt; b\),
			
@@ -1948,7 +1692,7 @@ called the {\bf quasistatic} approximation, and works provided we deal with
 
				
				 'slow enough' phenomena.
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<div class="example div" id="orge89f57b">
			
 
				
				+<div class="example div" id="orgd4a9b9d">
			
 
				
				 <p>
			
 
				
				 {\bf Example 7.9:}  infinitely long straight wire carries \(I(t)\).  Find
			
 
				
				 induced \({\bf E}\) field as a function of distance \(s\) from wire.
			
@@ -1983,7 +1727,7 @@ Reason:  in this case, we've overstepped the quasistatic limit.  We need
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Me.html
+++ b/build/emd_Me.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1888,7 +1632,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Me_Me.html
+++ b/build/emd_Me_Me.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1877,7 +1621,7 @@ Table of contents
 
				
				 <p>
			
 
				
				 Full set of equations for the electromagnetic field:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgc046634">
			
 
				
				+<div class="core div" id="org152d250">
			
 
				
				 <p>
			
 
				
				 {\bf Maxwell's equations} {\it (in vacuum)}
			
 
				
				 </p>
			
@@ -1893,7 +1637,7 @@ Full set of equations for the electromagnetic field:
 
				
				 <p>
			
 
				
				 Complement:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org29d2a12">
			
 
				
				+<div class="core div" id="org1c66368">
			
 
				
				 <p>
			
 
				
				 {\bf Force law}
			
 
				
				 \[
			
@@ -1917,7 +1661,7 @@ take divergence of \((iv)\).
 
				
				 <p>
			
 
				
				 Better way of writing:  all fields on left, all sources on right,
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgd4cf9e7">
			
 
				
				+<div class="core div" id="org1958d41">
			
 
				
				 \begin{align}
			
 
				
				   (i) &amp;{\boldsymbol \nabla} \cdot {\bf E} = \frac{\rho}{\varepsilon_0},
			
 
				
				   &amp;(iii) {\boldsymbol \nabla} \times {\bf E} + \frac{\partial {\bf B}}{\partial t} = 0, \\
			
@@ -1934,7 +1678,7 @@ Better way of writing:  all fields on left, all sources on right,
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Me_dc.html
+++ b/build/emd_Me_dc.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1884,7 +1628,7 @@ the continuity equation as
 
				
				 \]
			
 
				
				 The extra term would thus be eliminated if we were to put
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgf659cb5">
			
 
				
				+<div class="core div" id="orgff64dd3">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol \nabla} \times {\bf B} = \mu_0 {\bf J} + \mu_0 \varepsilon_0 \frac{\partial {\bf E}}{\partial t}
			
@@ -1908,7 +1652,7 @@ Real confirmation of Maxwell's theory:  1888, Hertz's experiments on propagation
 
				
				 <p>
			
 
				
				 Maxwell baptized this term the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgfe5954d">
			
 
				
				+<div class="core div" id="org4206404">
			
 
				
				 <p>
			
 
				
				 {\bf Displacement current}
			
 
				
				 \[
			
@@ -1943,7 +1687,7 @@ Flat surface:  OK, \(E = 0\) and \(I_{\mbox{enc}} = I\).  Balloon surface:  \(I
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Me_ebM.html
+++ b/build/emd_Me_ebM.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1913,7 +1657,7 @@ So for non-steady currents, the 'current enclosed by a loop' is ill-defined.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_Me_mc.html
+++ b/build/emd_Me_mc.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</ul>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1911,7 +1655,7 @@ Maxwell's equations {\bf beg} for magnetic charges.  But we've never found any!
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce.html
+++ b/build/emd_ce.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">emd.ce</span></h3>
			
 
				
				 
			
 
				
				 <div class="outline-text-3" id="text-emd_ce">
			
 
				
				-<details class="prereq" id="org51d68a7">
			
 
				
				-<summary id="orge489a25">
			
 
				
				+<details class="prereq" id="orge209dc2">
			
 
				
				+<summary id="org650a07d">
			
 
				
				 Prerequisites
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1884,8 +1628,8 @@ Prerequisites
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 
			
 
				
				-<details class="objectives" id="orgcbf139d">
			
 
				
				-<summary id="orga5dd4b1">
			
 
				
				+<details class="objectives" id="org4962fbd">
			
 
				
				+<summary id="org509fe5e">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1910,7 +1654,7 @@ Objectives
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce_amom.html
+++ b/build/emd_ce_amom.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1877,7 +1621,7 @@ Table of contents
 
				
				 <p>
			
 
				
				 The angular momentum of EM fields is directly given by
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orgec38a1b">
			
 
				
				+<div class="main div" id="org3de73d0">
			
 
				
				 <p>
			
 
				
				 {\bf Angular momentum of EM fields}
			
 
				
				 \[
			
@@ -1894,7 +1638,7 @@ The angular momentum of EM fields is directly given by
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce_ce.html
+++ b/build/emd_ce_ce.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1896,7 +1640,7 @@ This means that
 
				
				 \]
			
 
				
				 Since this is true for any volume, we have (re)derived the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgcc05f97">
			
 
				
				+<div class="core div" id="org20202cd">
			
 
				
				 <p>
			
 
				
				 {\bf Continuity equation}
			
 
				
				 \[
			
@@ -1924,7 +1668,7 @@ imposes a functional constraint on these sources: not {\it any} \(\rho\) and
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce_mom.html
+++ b/build/emd_ce_mom.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1889,7 +1633,7 @@ in which the first integral can be interpreted as the momentum stored in the EM
 
				
				 <p>
			
 
				
				 This is thus simply a conservation law for momentum, with
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orga07b125">
			
 
				
				+<div class="main div" id="org2bb42ec">
			
 
				
				 <p>
			
 
				
				 {\bf Momentum density in the EM fields}
			
 
				
				 \[
			
@@ -1901,7 +1645,7 @@ This is thus simply a conservation law for momentum, with
 
				
				 <p>
			
 
				
				 In a region in which the mechanical momentum is not changing due to external influences, we then have the
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org2f1f4d2">
			
 
				
				+<div class="main div" id="orgaafc4b4">
			
 
				
				 <p>
			
 
				
				 {\bf Continuity equation for EM momentum}
			
 
				
				 \[
			
@@ -1917,7 +1661,7 @@ In a region in which the mechanical momentum is not changing due to external inf
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce_mst.html
+++ b/build/emd_ce_mst.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</ul>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
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				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				 </ul>
			
@@ -1931,14 +1675,14 @@ and similarly for \({\boldsymbol B}\). We thus get
 
				
				 <p>
			
 
				
				 This expression can be greatly simplified by introducing the
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org36b6781">
			
 
				
				+<div class="main div" id="org9016172">
			
 
				
				 <p>
			
 
				
				 {\bf Maxwell stress tensor}
			
 
				
				 \[
			
 
				
				-  T<sub>ij</sub> ≡ ε<sub>0</sub> \left( E<sub>i</sub> E<sub>j</sub> - \frac{1}{2} δ<sub>ij</sub> E<sup>2\right</sup>)
			
 
				
				+  T_{ij} ≡ ε_0 \left( E_i E_j - \frac{1}{2} δ_{ij} E^2\right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{1}{\mu_0} \left( B<sub>i</sub> B<sub>j</sub> - \frac{1}{2} δ<sub>ij</sub> B<sup>2</sup> \right)</li>
			
 
				
				+<li>\frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} δ_{ij} B^2 \right)</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \]
			
@@ -1954,7 +1698,7 @@ The element \(T_{ij}\) represents the force per unit area in the $i$th direction
 
				
				 <p>
			
 
				
				 We then obtain
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org568f504">
			
 
				
				+<div class="main div" id="org39d7962">
			
 
				
				 <p>
			
 
				
				 {\bf EM force per unit volume}
			
 
				
				 \[
			
@@ -1966,7 +1710,7 @@ We then obtain
 
				
				 <p>
			
 
				
				 where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org29c117c">
			
 
				
				+<div class="main div" id="org384fd10">
			
 
				
				 <p>
			
 
				
				 {\bf Total force on charges in volume}
			
 
				
				 \[
			
@@ -1982,7 +1726,7 @@ where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_ce_poy.html
+++ b/build/emd_ce_poy.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1932,7 +1676,7 @@ But obviously,
 
				
				 \]
			
 
				
				 so we get
			
 
				
				 \[
			
 
				
				-{\bf E} ⋅ {\bf J} = -\frac{1}{2} \frac{\partial}{\partial t} \left( ε<sub>0</sub> E<sup>2</sup> + \frac{1}{\mu_0} B<sup>2</sup> \right)
			
 
				
				+{\bf E} ⋅ {\bf J} = -\frac{1}{2} \frac{\partial}{\partial t} \left( ε_0 E^2 + \frac{1}{\mu_0} B^2 \right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>\frac{1}{\mu_0} {\boldsymbol ∇} ⋅ ({\bf E} × {\bf B}).</li>
			
@@ -1943,14 +1687,14 @@ so we get
 
				
				 Substituting this in \ref{Gr(8.6)} and using the divergence theorem,
			
 
				
				 we obtain
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org27d4e56">
			
 
				
				+<div class="main div" id="org4fee5c1">
			
 
				
				 <p>
			
 
				
				 {\bf Poynting's theorem}
			
 
				
				 \[
			
 
				
				-  \frac{dW}{dt} = -\frac{d}{d t} ∫<sub>\cal V</sub> dτ \frac{1}{2} \left( ε<sub>0</sub> E<sup>2</sup> + \frac{1}{\mu_0} B<sup>2</sup> \right)
			
 
				
				+  \frac{dW}{dt} = -\frac{d}{d t} ∫_{\cal V} dτ \frac{1}{2} \left( ε_0 E^2 + \frac{1}{\mu_0} B^2 \right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{1}{\mu_0} \oint<sub>\cal S</sub> d{\bf a} ⋅ ({\bf E} × {\bf B})</li>
			
 
				
				+<li>\frac{1}{\mu_0} \oint_{\cal S} d{\bf a} ⋅ ({\bf E} × {\bf B})</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				   \label{Gr(8.9)}
			
@@ -1968,7 +1712,7 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
 
				
				 <p>
			
 
				
				 Energy per unit time, per unit area carried by EM fields:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org5a8440f">
			
 
				
				+<div class="core div" id="org31c447f">
			
 
				
				 <p>
			
 
				
				 {\bf Poynting vector}
			
 
				
				 \[
			
@@ -1981,7 +1725,7 @@ Energy per unit time, per unit area carried by EM fields:
 
				
				 <p>
			
 
				
				 We can thus express Poynting's theorem more compactly:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org70a18d5">
			
 
				
				+<div class="core div" id="org0a1de2b">
			
 
				
				 <p>
			
 
				
				 {\bf Poynting's theorem}
			
 
				
				 \[
			
@@ -1994,7 +1738,7 @@ We can thus express Poynting's theorem more compactly:
 
				
				 <p>
			
 
				
				 where we have defined the total
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgbd2e763">
			
 
				
				+<div class="core div" id="org18b8949">
			
 
				
				 <p>
			
 
				
				 {\bf Energy in electromagnetic fields}
			
 
				
				 \[
			
@@ -2017,7 +1761,7 @@ Then,
 
				
				 \]
			
 
				
				 so we get the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org785fb4f">
			
 
				
				+<div class="core div" id="org3f5d20d">
			
 
				
				 <p>
			
 
				
				 {\bf Poynting theorem (differential form)}
			
 
				
				 \[
			
@@ -2034,7 +1778,7 @@ and has a similar for to the continuity equation
 
				
				 
			
 
				
				 
			
 
				
				 
			
 
				
				-<div class="example div" id="org542e42c">
			
 
				
				+<div class="example div" id="org9d76705">
			
 
				
				 <p>
			
 
				
				 \paragraph{Example 8.1}  Current in a wire:  Joule heating.  Energy per unit time delivered to wire:  from Poynting.
			
 
				
				 Assuming that the field is uniform, the electric field parallel to the wire is
			
@@ -2066,7 +1810,7 @@ and the value is as expected.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_emw.html
+++ b/build/emd_emw.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</details>
			
 
				
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@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">emd.emw</span></h3>
			
 
				
				 
			
 
				
				 <div class="outline-text-3" id="text-emd_emw">
			
 
				
				-<details class="prereq" id="org90cfed8">
			
 
				
				-<summary id="orge5b2ad7">
			
 
				
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				+<summary id="orgd8f94af">
			
 
				
				 Prerequisites
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1885,8 +1629,8 @@ Prerequisites
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 
			
 
				
				-<details class="objectives" id="org2dafde2">
			
 
				
				-<summary id="org9224cce">
			
 
				
				+<details class="objectives" id="org8ebd2c8">
			
 
				
				+<summary id="org56a0c80">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1914,7 +1658,7 @@ Objectives
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_emw_ep.html
+++ b/build/emd_emw_ep.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1905,7 +1649,7 @@ so for a monochromatic EM plan wave,
 
				
				 \]
			
 
				
				 or more succinctly:
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org96a5e5a">
			
 
				
				+<div class="main div" id="org5ab2d39">
			
 
				
				 <p>
			
 
				
				 {\bf Poynting vector of a monochromatic EM wave}
			
 
				
				 \[
			
@@ -1921,7 +1665,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
 
				
				 <p>
			
 
				
				 Similary, we get the
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orgcfdec88">
			
 
				
				+<div class="main div" id="org703b070">
			
 
				
				 <p>
			
 
				
				 {\bf Momentum density of a monochromatic EM wave}
			
 
				
				 \[
			
@@ -1959,7 +1703,7 @@ The {\it radiation pressure} is the momentum transfer per unit area per unit of
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_emw_mpw.html
+++ b/build/emd_emw_mpw.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1906,7 +1650,7 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
 
				
				 Generalizing to propagation in the direction of an arbitrary wavevector
			
 
				
				 \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orga2608fb">
			
 
				
				+<div class="core div" id="orgf8f14a8">
			
 
				
				 <p>
			
 
				
				 {\bf E and B fields for a monochromatic EM plane wave}
			
 
				
				 \[
			
@@ -1937,7 +1681,7 @@ or if you prefer explicit real parts (adding a possible phase shift \(\delta\)):
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emd_emw_we.html
+++ b/build/emd_emw_we.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1903,7 +1647,7 @@ These take the form of coupled first-order partial differential equations for \(
 
				
				 Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
			
 
				
				 we get the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgde95589">
			
 
				
				+<div class="core div" id="org6e2c86d">
			
 
				
				 <p>
			
 
				
				 {\bf Wave equations for electric and magnetic fields in vacuum}
			
 
				
				 \[
			
@@ -1946,7 +1690,7 @@ the actual electric and magnetic fields are given by the real part.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm.html
+++ b/build/emdm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				 </ul>
			
@@ -1886,7 +1630,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_Me.html
+++ b/build/emdm_Me.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
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@@ -565,29 +502,8 @@ Table of contents
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1886,7 +1630,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_Me_Mem.html
+++ b/build/emdm_Me_Mem.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1910,7 +1654,7 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
 
				
				 \]
			
 
				
				 We therefore have the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgb5c72da">
			
 
				
				+<div class="core div" id="orgb555ebf">
			
 
				
				 <p>
			
 
				
				 {\bf Polarization current density}
			
 
				
				 \[
			
@@ -1928,7 +1672,7 @@ the polarization current is the result of linear motion of charge when
 
				
				 polarization changes).  We can check consistency with the continuity equation
			
 
				
				 associated to the conservation of bound charges:
			
 
				
				 </p>
			
 
				
				-<aside id="org7ce3b70">
			
 
				
				+<aside id="org86c5ff2">
			
 
				
				 <p>
			
 
				
				 Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current
			
 
				
				   \({\boldsymbol J}_b\) but this is not the convention used here.
			
@@ -1951,7 +1695,7 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
 
				
				 In view of this:  total charge density can be separated into 2 parts,
			
 
				
				 {\it free} and {\it bound}:
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org3b2083c">
			
 
				
				+<div class="main div" id="orgf8c82b2">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     \rho = \rho_f + \rho_b = \rho_f - {\boldsymbol \nabla} \cdot {\bf P}
			
@@ -1964,10 +1708,10 @@ In view of this:  total charge density can be separated into 2 parts,
 
				
				 and current can be separated into three parts, {\it free}, {\it bound} and
			
 
				
				 {\it polarization}:
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org09ed727">
			
 
				
				+<div class="main div" id="org4054380">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-  {\bf J} = {\bf J}<sub>f</sub> + {\bf J}<sub>b</sub> + {\bf J}<sub>p</sub> = {\bf J}<sub>f</sub> + {\boldsymbol ∇} × {\bf M}
			
 
				
				+  {\bf J} = {\bf J}_f + {\bf J}_b + {\bf J}_p = {\bf J}_f + {\boldsymbol ∇} × {\bf M}
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				 <li>\frac{∂ {\bf P}}{∂ t}.</li>
			
@@ -1988,7 +1732,7 @@ Gauss's law:  can be rewritten
 
				
				 \]
			
 
				
				 where (as in static case)
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org508fb0a">
			
 
				
				+<div class="core div" id="orgf78b92c">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
			
@@ -2000,10 +1744,10 @@ where (as in static case)
 
				
				 <p>
			
 
				
				 Ampère's law including Maxwell's term:
			
 
				
				 \[
			
 
				
				-{\boldsymbol ∇} × {\bf B} = μ<sub>0</sub> \left( {\bf J}<sub>f</sub> + {\boldsymbol ∇} × {\bf M}
			
 
				
				+{\boldsymbol ∇} × {\bf B} = μ_0 \left( {\bf J}_f + {\boldsymbol ∇} × {\bf M}
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>\frac{∂ {\bf P}}{∂ t} \right) + μ<sub>0</sub> ε<sub>0</sub> \frac{∂ {\bf E}}{∂ t},</li>
			
 
				
				+<li>\frac{∂ {\bf P}}{∂ t} \right) + μ_0 ε_0 \frac{∂ {\bf E}}{∂ t},</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				 \]
			
@@ -2014,7 +1758,7 @@ or
 
				
				 \]
			
 
				
				 where as before
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org6879249">
			
 
				
				+<div class="core div" id="org513c514">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
			
@@ -2032,7 +1776,7 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
 
				
				 <p>
			
 
				
				 In terms of free charges and currents, we thus get
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgb7d4703">
			
 
				
				+<div class="core div" id="org686ea33">
			
 
				
				 <p>
			
 
				
				 {\bf Maxwell's equations {\it (in matter)}}
			
 
				
				 </p>
			
@@ -2058,7 +1802,7 @@ Must be complemented by the {\bf constitutive relations} giving \({\bf D}\) and
 
				
				 in terms of \({\bf E}\) and \({\bf B}\).
			
 
				
				 For the restricted case of linear media:
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org30a7942">
			
 
				
				+<div class="main div" id="org6accc1d">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\bf P} = \varepsilon_0 \chi_e {\bf E}, \hspace{1cm}
			
@@ -2082,7 +1826,7 @@ where \(\varepsilon \equiv \varepsilon_0(1 + \chi_e)\) and \(\mu \equiv \mu_0 (1
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_Me_bc.html
+++ b/build/emdm_Me_bc.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1877,7 +1621,7 @@ Table of contents
 
				
				 <p>
			
 
				
				 Discontinuities between different media, deduced from
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgb5cfb31">
			
 
				
				+<div class="core div" id="org18c9c85">
			
 
				
				 <p>
			
 
				
				 {\bf Maxwell's equations {\it (in matter)}, integral form}
			
 
				
				 </p>
			
@@ -1955,7 +1699,7 @@ These are basis of theory of reflection and refraction.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm.html
+++ b/build/emdm_emwm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1889,7 +1633,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_ad.html
+++ b/build/emdm_emwm_ad.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1885,7 +1629,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_ad_c.html
+++ b/build/emdm_emwm_ad_c.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1981,7 +1725,7 @@ so the final form of the fields is
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_plm.html
+++ b/build/emdm_emwm_plm.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1912,7 +1656,7 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
 
				
				 \]
			
 
				
				 where the index of refraction of the material is defined as
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org4e4a2f7">
			
 
				
				+<div class="main div" id="orgc00345d">
			
 
				
				 <p>
			
 
				
				 {\bf Index of refraction}
			
 
				
				 \[
			
@@ -1956,7 +1700,7 @@ I = \frac{1}{2} \varepsilon v E_0^2
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refl.html
+++ b/build/emdm_emwm_refl.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1900,7 +1644,7 @@ Detailed study:  starts from boundary conditions \ref{Gr(7.64)},
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refl_Ba.html
+++ b/build/emdm_emwm_refl_Ba.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1880,7 +1624,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refl_Fe.html
+++ b/build/emdm_emwm_refl_Fe.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1881,7 +1625,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refl_ni.html
+++ b/build/emdm_emwm_refl_ni.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
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				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
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				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				 </ul>
			
@@ -1972,7 +1716,7 @@ R + T = 1.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refl_oi.html
+++ b/build/emdm_emwm_refl_oi.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1912,7 +1656,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
 
				
				 <p>
			
 
				
				 From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org5b0d3cd">
			
 
				
				+<div class="core div" id="orgefbfc7d">
			
 
				
				 <p>
			
 
				
				 {\bf First law of reflection:}
			
 
				
				 the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
			
@@ -1927,7 +1671,7 @@ Specializing (\ref{eq:RTObliquek}) to our notations, we have
 
				
				 with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
			
 
				
				 and the angle of refraction (\(\theta_T\)) obey the following laws:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgad4f6b0">
			
 
				
				+<div class="core div" id="org13fc947">
			
 
				
				 <p>
			
 
				
				 {\bf Law of reflection}
			
 
				
				 \[
			
@@ -1985,7 +1729,7 @@ while the third equation becomes
 
				
				 \]
			
 
				
				 Writing everything in terms of the incident amplitude, we get
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org969c30d">
			
 
				
				+<div class="main div" id="orgd7a540b">
			
 
				
				 <p>
			
 
				
				 {\bf Fresnel's equations for reflection and transmission amplitudes (parallel case)}
			
 
				
				 \[
			
@@ -2005,7 +1749,7 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
 
				
				 Behaviour: for \(\theta_I = 0\) we recover (\ref{Gr(9.82)}).
			
 
				
				 For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orgd0455e3">
			
 
				
				+<div class="main div" id="orgdb6468b">
			
 
				
				 <p>
			
 
				
				 {\bf Brewster's angle {\it (at which the reflected wave amplitude vanishes)}}
			
 
				
				   \[
			
@@ -2042,7 +1786,7 @@ Of course, we get \(R + T = 1\) as expected.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_refr.html
+++ b/build/emdm_emwm_refr.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1881,7 +1625,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_wg.html
+++ b/build/emdm_emwm_wg.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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@@ -1887,7 +1631,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_wg_c.html
+++ b/build/emdm_emwm_wg_c.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
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				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
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@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1907,7 +1651,7 @@ where \(A\) is a constant amplitude. Substituting and taking the real part,
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_wg_gw.html
+++ b/build/emdm_emwm_wg_gw.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1931,7 +1675,7 @@ with an identical equation for \(B_z\). If \(E_z = 0\) the waves are called {\bf
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emdm_emwm_wg_r.html
+++ b/build/emdm_emwm_wg_r.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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				 </ul>
			
@@ -1940,7 +1684,7 @@ which is {\it greater} than \(c\). The energy of the wave however propagates at
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emf.html
+++ b/build/emf.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">emf</span></h2>
			
 
				
				 
			
 
				
				 <div class="outline-text-2" id="text-emf">
			
 
				
				-<details class="prereq" id="org720fb76">
			
 
				
				-<summary id="org8fa28e8">
			
 
				
				+<details class="prereq" id="org0b4147b">
			
 
				
				+<summary id="orgaa9a8c2">
			
 
				
				 Prerequisites
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1884,8 +1628,8 @@ Prerequisites
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 
			
 
				
				-<details class="objectives" id="orgb2961ae">
			
 
				
				-<summary id="orga6c8829">
			
 
				
				+<details class="objectives" id="orgd0127b4">
			
 
				
				+<summary id="orgf210d58">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1908,7 +1652,7 @@ Objectives
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emf_g.html
+++ b/build/emf_g.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
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				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
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				-<a href="#org788e483">Before Coulomb</a>
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				-<a href="#org359fd13">Current status</a>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
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				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
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				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
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@@ -1905,7 +1649,7 @@ implementing a <b>gauge transformation</b>.
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
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@@ -1,7 +1,7 @@
 
				
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				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				 </ul>
			
@@ -1904,7 +1648,7 @@ Although Gauss's law looks nice in the Coulomb gauge, Amp{\`e}re-Maxwell does no
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emf_g_Lg.html
+++ b/build/emf_g_Lg.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
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				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
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				-<a href="#org1f82edc">Coulomb</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
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				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1890,7 +1634,7 @@ while the equation for \(V\) becomes
 
				
				 \]
			
 
				
				 These can be written compactly upon introducing a new operator: the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org07a44ab">
			
 
				
				+<div class="core div" id="orgd5ba96e">
			
 
				
				 <p>
			
 
				
				 {\bf d'Alembertian operator}
			
 
				
				 \[
			
@@ -1903,7 +1647,7 @@ These can be written compactly upon introducing a new operator: the
 
				
				 <p>
			
 
				
				 so we get the
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="orgc7c0452">
			
 
				
				+<div class="core div" id="org15005e7">
			
 
				
				 <p>
			
 
				
				 {\bf Inhomogeneous Maxwell equations (Lorenz gauge)}
			
 
				
				 \[
			
@@ -1940,7 +1684,7 @@ we have by direct inspection
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/emf_svp.html
+++ b/build/emf_svp.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1891,7 +1635,7 @@ Useful strategy: represent fields in terms of potentials.
 
				
				 <p>
			
 
				
				 Easiest:
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org2047afa">
			
 
				
				+<div class="core div" id="org389d31f">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
			
@@ -1907,7 +1651,7 @@ Putting this into Faraday's law gives
 
				
				 \]
			
 
				
				 so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \nabla} V\)) so we get
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org135e92c">
			
 
				
				+<div class="core div" id="orgbbcf54f">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol E} = -{\boldsymbol \nabla} V - \frac{\partial {\boldsymbol A}}{\partial t}
			
@@ -1920,7 +1664,7 @@ so this can be written as the gradient of a scalar (by choice: \(-{\boldsymbol \
 
				
				 <p>
			
 
				
				 Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting (\ref{eq:E_from_Potentials}) into Gauss's law gives
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="org020a783">
			
 
				
				+<div class="main div" id="org2d36baf">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol \nabla}^2 V + \frac{\partial}{\partial t} {\boldsymbol \nabla} \cdot {\boldsymbol A} = -\frac{\rho}{\varepsilon_0}
			
@@ -1936,13 +1680,13 @@ whereas Amp{\`ere}-Maxwell becomes
 
				
				 \]
			
 
				
				 which becomes after simple rearrangement and use of the identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orga9e7111">
			
 
				
				+<div class="main div" id="orga7cdd8b">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				-  \left( {\boldsymbol ∇}<sup>2</sup> {\boldsymbol A} - μ<sub>0</sub> ε<sub>0</sub> \frac{∂<sup>2</sup> {\boldsymbol A}}{∂ t<sup>2</sup>} \right)
			
 
				
				+  \left( {\boldsymbol ∇}^2 {\boldsymbol A} - μ_0 ε_0 \frac{∂^2 {\boldsymbol A}}{∂ t^2} \right)
			
 
				
				 </p>
			
 
				
				 <ul class="org-ul">
			
 
				
				-<li>{\boldsymbol ∇} \left({\boldsymbol ∇} ⋅ {\boldsymbol A} + μ<sub>0</sub> ε<sub>0</sub> \frac{\partial V}{\partial t} \right) = -μ<sub>0</sub> {\boldsymbol J}</li>
			
 
				
				+<li>{\boldsymbol ∇} \left({\boldsymbol ∇} ⋅ {\boldsymbol A} + μ_0 ε_0 \frac{\partial V}{\partial t} \right) = -μ_0 {\boldsymbol J}</li>
			
 
				
				 </ul>
			
 
				
				 <p>
			
 
				
				   \label{eq:LaplacianA}
			
@@ -1959,7 +1703,7 @@ which becomes after simple rearrangement and use of the identity \({\boldsymbol
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/ems.html
+++ b/build/ems.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
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				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
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@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
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				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
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				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
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				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</details>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
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				-
			
 
				
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				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
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				-<ul>
			
 
				
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				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-</details>
			
 
				
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				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				-<details>
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
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				-</li>
			
 
				
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				-</details>
			
 
				
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				 </ul>
			
@@ -1888,7 +1632,7 @@ Table of contents
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/ems_ca.html
+++ b/build/ems_ca.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
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				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
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				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
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				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
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				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
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				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
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@@ -1875,8 +1619,8 @@ Table of contents
 
				
				 </svg></a><span class="headline-id">ems.ca</span></h3>
			
 
				
				 
			
 
				
				 <div class="outline-text-3" id="text-ems_ca">
			
 
				
				-<details class="prereq" id="orga9b4667">
			
 
				
				-<summary id="org6a495fc">
			
 
				
				+<details class="prereq" id="org9f1c7db">
			
 
				
				+<summary id="orgbf053b0">
			
 
				
				 Prerequisites
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1884,8 +1628,8 @@ Prerequisites
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 
			
 
				
				-<details class="objectives" id="org20c94d0">
			
 
				
				-<summary id="org981132c">
			
 
				
				+<details class="objectives" id="org06b35e7">
			
 
				
				+<summary id="org6416a57">
			
 
				
				 Objectives
			
 
				
				 </summary>
			
 
				
				 <ul class="org-ul">
			
@@ -1910,7 +1654,7 @@ Objectives
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/ems_ca_fe.html
+++ b/build/ems_ca_fe.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
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				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -565,29 +502,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
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				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
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				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
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				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-<details>
			
 
				
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				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
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				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
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				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
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@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				-
			
 
				
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				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
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				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
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				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
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				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
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				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
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				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
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				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
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				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
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				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
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				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
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				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
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				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
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				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
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				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
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				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
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				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
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				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1878,22 +1622,19 @@ Table of contents
 
				
				 <p>
			
 
				
				 A generic configuration of static charges coupled via the Coulomb interaction
			
 
				
				 defines an electrostatic problem, whose solution is in principle obtained
			
 
				
				-from calculating either the field according to (\ref{eq:E_from_rho}),
			
 
				
				-</p>
			
 
				
				-<div class="main div" id="orgd9c6ec8">
			
 
				
				-<p>
			
 
				
				-\[
			
 
				
				-    {\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
			
 
				
				-    \tag{\ref{eq:E_from_rho}}
			
 
				
				-  \]
			
 
				
				+from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
			
 
				
				 </p>
			
 
				
				+<div class="main div" id="orgb912407">
			
 
				
				+\begin{equation*}
			
 
				
				+  {\bf E} ({\bf r}) = \frac{1}{4\pi\varepsilon_0} \int_{\mathbb{R}^3} d\tau' \rho({\bf r}') \frac{{\bf r} - {\bf r}'}{|{\bf r} - {\bf r}'|^3}
			
 
				
				+\end{equation*}
			
 
				
				 
			
 
				
				 </div>
			
 
				
				 <p>
			
 
				
				 or (often simpler) by calculating the electrostatic potential, using either the
			
 
				
				 explicit construction (\ref{eq:V_from_rho})
			
 
				
				 </p>
			
 
				
				-<div class="main div" id="orgabd23e7">
			
 
				
				+<div class="main div" id="orgc09a05f">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     V({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\mathbb{R}^3} d\tau' \frac{\rho({\bf r}')}{|{\bf r} - {\bf r}'|}.
			
@@ -1909,7 +1650,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
 
				
				 'local' (differential) condition (Poisson's equation) (\ref{eq:Poisson})
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<div class="core div" id="orgb65e1cf">
			
 
				
				+<div class="core div" id="orgbe52068">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol \nabla}^2 V = -\frac{\rho}{\varepsilon_0}.
			
@@ -1923,7 +1664,7 @@ condition (\ref{Gr(2.20)}) can be expressed as the single
 
				
				 In the specific case where the charge density vanishes, we fall back onto the simpler
			
 
				
				 Laplace equation
			
 
				
				 </p>
			
 
				
				-<div class="core div" id="org0f820c6">
			
 
				
				+<div class="core div" id="orgb4303af">
			
 
				
				 <p>
			
 
				
				 \[
			
 
				
				     {\boldsymbol \nabla}^2 V = 0
			
@@ -1945,7 +1686,7 @@ Laplace equation
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/ems_ca_fe_L.html
+++ b/build/ems_ca_fe_L.html
@@ -1,7 +1,7 @@
 
				
				 <!DOCTYPE html>
			
 
				
				 <html lang="en">
			
 
				
				 <head>
			
 
				
				-<!-- 2022-02-07 Mon 08:02 -->
			
 
				
				+<!-- 2022-02-08 Tue 06:55 -->
			
 
				
				 <meta charset="utf-8">
			
 
				
				 <meta name="viewport" content="width=device-width, initial-scale=1">
			
 
				
				 <title>Pre-Quantum Electrodynamics</title>
			
@@ -348,58 +348,12 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org788e483">Before Coulomb</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org8b037d5">Cavendish's experiment</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org1f82edc">Coulomb</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#org359fd13">Current status</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_p">Work; Pairwise Energy</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_ga">Generic assembly</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_efo_e_cl">Crystal lattices</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -427,25 +381,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./ems_es_ef_Gl.html#ems_es_ef_Gl">Gauss's Law: the divergence of \({\bf E}\)</a><span class="headline-id">ems.es.ef.Gl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_fl">Field Lines, Flux and Gauss's Law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_es_ef_Gl_ex">Examples of applications of Gauss's law</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -455,7 +392,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_ep.html#ems_es_ep">Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				+<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -492,7 +429,7 @@ Table of contents
 
				
				 
			
 
				
				 <details>
			
 
				
				 <summary>
			
 
				
				-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy</a><span class="headline-id">ems.es.e</span>
			
 
				
				+<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
			
 
				
				 
			
 
				
				 
			
 
				
				 </summary>
			
@@ -564,30 +501,9 @@ Table of contents
 
				
				 
			
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details open="">
			
 
				
				-<summary class="toc-currentpage">
			
 
				
				+<li class="toc-currentpage">
			
 
				
				 <a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_1d">The Laplace Equation in One Dimension</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_2d">The Laplace Equation in Two Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#ems_ca_fe_L_3d">The Laplace Equation in Three Dimensions</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
			
@@ -871,33 +787,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_esm_di_ld.html#emsm_esm_di_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.di.ld</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_d_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_bvp">Boundary Value Problems with Linear Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_e">Energy in Dielectric Systems</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_esm_di_ld_f">Forces on Dielectrics</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -926,21 +817,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org65874b3">Why is Ferromagnetism such an intriguing phenomenon?</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
			
@@ -989,25 +867,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_dp">A Deceptive Parallel</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#emsm_msm_H_A_elm">Energy in Linear Media</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1599,37 +1460,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_dc_d2.html#c_m_dc_d2">Second Derivatives</a><span class="headline-id">c.m.dc.d2</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#orge025182">Divergence of gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgacb930d">Curl of a gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org6caee98">Gradient of the divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgb5da747">Divergence of a curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgebcbadc">Curl of curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1645,29 +1477,8 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_ic_lsv.html#c_m_ic_lsv">Line, Surface and Volume Integrals</a><span class="headline-id">c.m.ic.lsv</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#org638a76f">Line Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#orgd8e925a">Surface Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#org5c24b4a">Volume Integrals</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_ic_ftc.html#c_m_ic_ftc">The Fundamental Theorem of Calculus</a><span class="headline-id">c.m.ic.ftc</span>
			
@@ -1703,62 +1514,12 @@ Table of contents
 
				
				 </summary>
			
 
				
				 <ul>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_sph.html#c_m_cs_sph">Spherical Coordinates</a><span class="headline-id">c.m.cs.sph</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_sph_curl">Curl</a>
			
 
				
				-
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-<a href="#c_m_cs_sph_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_cs_cyl.html#c_m_cs_cyl">Cylindrical Coordinates</a><span class="headline-id">c.m.cs.cyl</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_grad">Gradient</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_div">Divergence</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_curl">Curl</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_cs_cyl_lap">Laplacian</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				 <a href="./c_m_cs_hyp.html#c_m_cs_hyp">Hyperbolic Coordinates</a><span class="headline-id">c.m.cs.hyp</span>
			
@@ -1807,25 +1568,8 @@ Table of contents
 
				
				 
			
 
				
				 </li>
			
 
				
				 <li>
			
 
				
				-
			
 
				
				-<details>
			
 
				
				-<summary>
			
 
				
				 <a href="./c_m_vf_pot.html#c_m_vf_pot">Potentials</a><span class="headline-id">c.m.vf.pot</span>
			
 
				
				 
			
 
				
				-
			
 
				
				-</summary>
			
 
				
				-<ul>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_irrot">Theorem 1:  Curl-less (irrotational) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-<li>
			
 
				
				-<a href="#c_m_vf_pot_solen">Theorem 2:  Divergence-less (solenoidal) fields</a>
			
 
				
				-
			
 
				
				-</li>
			
 
				
				-
			
 
				
				-</ul>
			
 
				
				-</details>
			
 
				
				 </li>
			
 
				
				 
			
 
				
				 </ul>
			
@@ -1868,7 +1612,7 @@ Table of contents
 
				
				 </ul>
			
 
				
				 </details>
			
 
				
				 </nav>
			
 
				
				-<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_L_1d.html">The Laplace Equation in One Dimension&emsp;<small>[ems.ca.fe.L.1d]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_L" class="outline-5">
			
 
				
				+<ul class="navigation-links"><li>Prev:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li><li>Next:&nbsp;<a href="ems_ca_fe_g.html">Green's Identities&emsp;<small>[ems.ca.fe.g]</small></a></li><li>Up:&nbsp;<a href="ems_ca_fe.html">Fundamental Equations for the Electrostatic Potential&emsp;<small>[ems.ca.fe]</small></a></li></ul><div id="outline-container-ems_ca_fe_L" class="outline-5">
			
 
				
				 <h5 id="ems_ca_fe_L">The Laplace Equation<a class="headline-permalink" href="./ems_ca_fe_L.html#ems_ca_fe_L"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
			
 
				
				   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
			
 
				
				   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
			
@@ -1954,7 +1698,7 @@ are necessarily positive, we thus require \(f_x &gt; 0\), \(f_y &gt; 0\) and \(f
 
				
				 of the \(f_x + f_y + f_z = 0\) condition above.
			
 
				
				 </p>
			
 
				
				 
			
 
				
				-<div class="info div" id="org0be6d8d">
			
 
				
				+<div class="info div" id="orga2b5411">
			
 
				
				 <p>
			
 
				
				 <b>Earnshaw's theorem</b> <br>
			
 
				
				 Since solutions to Laplace's equation have no local minimum,
			
@@ -2044,7 +1788,7 @@ This all feels a bit amateurish and not very systematic. Can we be more precise
 
				
				 
			
 
				
				 <hr><div id="postamble" class="status">
			
 
				
				 <p class="author">Author: Jean-Sébastien Caux</p>
			
 
				
				-<p class="date">Created: 2022-02-07 Mon 08:02</p>
			
 
				
				+<p class="date">Created: 2022-02-08 Tue 06:55</p>
			
 
				
				 <p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
			
 
				
				 </div>
			
 
				
				 
			
--- a/build/ems_ca_fe_g.html
+++ b/build/ems_ca_fe_g.html