Pre-Quantum Electrodynamics

Table of contents

Introductionin
- Prefacein.p
- Tips for the readerin.t
  - Contextual colorsin.t.c
Electromagnetostaticsems
- Electrostaticsems.es
  - Electric Chargeems.es.ec
    
    Basicsems.es.ec.b
    
    Conservationems.es.ec.c
    
    Quantizationems.es.ec.q
    
    Structureems.es.ec.s
  - Electric Force and Energyems.es.efo
    
    Coulomb's Lawems.es.efo.cl
    
    Principle of Superpositionems.es.efo.ps
    
    Experimental Investigationsems.es.efo.exp
    
    Energy in Systems of Point Chargesems.es.efo.e
  - Electrostatic Fieldsems.es.ef
    
    Electrostatic Field of Point Chargesems.es.ef.pc
    
    Electrostatic Field of Continuous Charge Distributionsems.es.ef.ccd
    
    The Curl of \({\bf E}\)ems.es.ef.cE
    
    Gauss's Law: the divergence of \({\bf E}\)ems.es.ef.Gl
  - The Electrostatic Potentialems.es.ep
    
    Definitionems.es.ep.d
    
    Field in terms of the potentialems.es.ep.fp
    
    Comments on the Electrostatic Potentialems.es.ep.c
    
    Example calculations for the potentialems.es.ep.ex
    
    The Poisson Equation and the Laplace Equationems.es.ep.PL
    
    Electrostatic Boundary Conditionsems.es.ep.bc
  - Electrostatic Energy from the Potentialems.es.e
    
    The Energy of a Point Charge Distributionems.es.e.pcd
    
    The Energy of a Continuous Charge Distributionems.es.e.ccd
    
    Comments on Electrostatic Energyems.es.e.c
  - Conductorsems.es.c
    
    Propertiesems.es.c.p
    
    Induced Chargesems.es.c.ic
    
    Surface Charge and the Force on a Conductorems.es.c.sc
    
    Capacitorsems.es.c.cap
- Calculating or Approximating the Electrostatic Potentialems.ca
  - Fundamental Equations for the Electrostatic Potentialems.ca.fe
    
    The Laplace Equationems.ca.fe.L
    
    Green's Identitiesems.ca.fe.g
    
    Uniqueness of Solution to Poisson's Equationems.ca.fe.uP
  - The Method of Imagesems.ca.mi
    
    Induced Surface Chargesems.ca.mi.isc
    
    Force and Energyems.ca.mi.fe
    
    Other Image Problemsems.ca.mi.o
  - Separation of Variablesems.ca.sv
    
    Cartesian Coordinatesems.ca.sv.car
    
    Cylindrical Coordinatesems.ca.sv.cyl
    
    Spherical Coordinatesems.ca.sv.sph
  - The Multipole Expansionems.ca.me
    
    Approximate Potential at Large Distanceems.ca.me.a
    
    Monopole and Dipole Termsems.ca.me.md
    
    Higher Momentsems.ca.me.h
    
    The Electric Field of a Dipoleems.ca.me.Ed
    
    The Electric Field of a Quadrupoleems.ca.me.Eq
- Magnetostaticsems.ms
  - Charges in Motion: the Lorentz Force Lawems.ms.lf
    
    Point Chargeems.ms.lf.pc
    
    Currentsems.ms.lf.c
  - Steady Currents: the Biot-Savart Lawems.ms.BS
    
    The Magnetic Field issuing from a Steady Currentems.ms.BS.sc
  - Divergence and Curl of \({\bf B}\)ems.ms.dcB
    
    Straight-line Currentsems.ms.dcB.sc
    
    Divergence and Curl of \({\bf B}\) from Biot-Savartems.ms.dcB.BS
  - The Vector Potentialems.ms.vp
    
    Magnetic Boundary Conditionsems.ms.vp.mbc
    
    Multipole Expansion of the Vector Potentialems.ms.vp.me
    
    Comparison of Electrostatics and Magnetostaticsems.ms.vp.comp
    
    The Levi-Civita Symbolems.ms.vp.LC
Electromagnetostatics in matteremsm
- A proper definition of "statics"emsm.esm.s
- Electrostatics in matteremsm.esm
  - Polarizationemsm.esm.p
  - Dielectricsemsm.esm.d
  - The Field of a Polarized Objectemsm.esm.fpo
    
    Physical Interpretation of Bound Chargesemsm.esm.fpo.pibc
    
    The Field Inside a Dielectricemsm.esm.fpo.fid
  - The Electric Displacementemsm.esm.D
    
    Boundary Conditionsemsm.esm.D.bc
  - Dielectricsemsm.esm.di
    
    Linear Dielectricsemsm.esm.di.ld
- Magnetostatics in matteremsm.msm
  - Magnetizationemsm.msm.m
    
    Diamagnetism, Paramagnetism, Ferromagnetismemsm.msm.m.dpf
    
    Torques and Forces on Magnetic Dipolesemsm.msm.m.fdi
    
    Effect of Magnetic Field on Atomic Orbitsemsm.msm.a
  - The Field of a Magnetized Objectemsm.msm.fmo
    
    Bound Currentsemsm.msm.fmo.bc
    
    Physical Interpretation of Bound Currentsemsm.msm.fmo.pibc
    
    The Magnetic Field Inside Matteremsm.msm.fmo.fim
  - The H Fieldemsm.msm.H
    
    Ampère's Law in Magnetized Materialsemsm.msm.H.A
  - Linear and Nonlinear Mediaemsm.msm.lnlm
    
    Magnetic Susceptibility and Permeabilityemsm.msm.lnlm.sp
    
    Ferromagnetismemsm.msm.lnlm.fm
Electromagnetodynamicsemd
- Induction: Faraday's Lawemd.Fl
  - Faraday's Lawemd.Fl.Fl
  - The Induced Electric Fieldemd.Fl.ief
  - Inductanceemd.Fl.i
  - Energy in Magnetic Fieldsemd.Fl.e
- Maxwell's Equationsemd.Me
  - Electrodynamics Before Maxwellemd.Me.ebM
  - Maxwell's Correction to Ampère's Law; the Displacement Currentemd.Me.dc
  - Maxwell's Equationsemd.Me.Me
  - Magnetic Chargeemd.Me.mc
- Charge and Energy Flowsemd.ce
  - The Continuity Equationemd.ce.ce
  - Poynting's Theorem; the Poynting Vectoremd.ce.poy
  - Maxwell's Stress Tensoremd.ce.mst
  - Momentumemd.ce.mom
  - Angular Momentumemd.ce.amom
- Electromagnetic waves in vacuumemd.emw
  - The Wave Equationemd.emw.we
  - Monochromatic Plane Wavesemd.emw.mpw
  - Energy and Momentumemd.emw.ep
Electromagnetodynamics in Matteremdm
- Maxwell's Equations in Matteremdm.Me
  - Maxwell's Equations in Matteremdm.Me.Mem
  - Boundary Conditionsemdm.Me.bc
- Electromagnetic Waves in Matteremdm.emwm
  - Propagation in Linear Mediaemdm.emwm.plm
  - Refractionemdm.emwm.refr
  - Reflection and Transmissionemdm.emwm.refl
    
    Normal Incidenceemdm.emwm.refl.ni
    
    Oblique Incidenceemdm.emwm.refl.oi
    
    Fresnel's Equationsemdm.emwm.refl.Fe
    
    Brewster's Angleemdm.emwm.refl.Ba
  - Absorption and Dispersionemdm.emwm.ad
    
    EM Waves in Conductorsemdm.emwm.ad.c
  - Waveguidesemdm.emwm.wg
    
    Guided wavesemdm.emwm.wg.gw
    
    Rectangular Waveguidesemdm.emwm.wg.r
    
    Coaxial Linesemdm.emwm.wg.c
Electromagnetic Fieldsemf
- Scalar and Vector Potentialsemf.svp
- Gauge Freedom and Choicesemf.g
  - Coulomb Gaugeemf.g.Cg
  - Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equationsemf.g.Lg
Relativistic Electrodynamicsred
- Special Relativityred.sr
  - Postulates and their consequencesred.sr.p
  - Lorentz Transformationsred.sr.Lt
  - Covariant and Contravariant Four-Vectorsred.sr.4v
- Relativistic Mechanicsred.rm
  - Proper Time and Proper Velocityred.rm.pt
  - Relativistic Momentum and Energyred.rm.rme
  - Relativistic version of Newton's Laws; the Minkowski Forcered.rm.Mf
- Relativistic Electromagnetismred.rem
  - Magnetism as a Relativistic Effectred.rem.mre
  - Lorentz Transformation of Electromagnetic Fieldsred.rem.Ltf
  - The Field Tensorred.rem.Fmunu
  - Maxwell's Equations in Relativistic Notationred.rem.Me
Quantum Electrodynamicsqed
- QED todayqed.t
Diagnosticsd
- Diagnostics: Mathematical Preliminariesd.m
- Diagnostics: Electromagnetostaticsd.ems
- Diagnostics: Calculating or Approximating the Electostatic Potentiald.ems.ca
- Diagnostics: Electromagnetostatics in Matterd.emsm
- Diagnostics: Magnetostaticsd.ems.ms
- Diagnostics: Magnetostatics in Matterd.emsm.msm
- Diagnostics: Electromagnetodynamicsd.emd
- Diagnostics: Conservation Lawsd.emd.ce
- Diagnostics: Electromagnetic Wavesd.emd.emw
- Diagnostics: Potentials, Gauges and Fieldsd.emf
- Diagnostics: Relativistic Electrodynamicsd.red
Appendicesa
- Literaturea.l
Compendiumc
- Mathematicsc.m
  - Vector Analysisc.m.va
    
    Notation and algebraic propertiesc.m.va.n
    
    Scalar productc.m.va.sp
    
    Cross productc.m.va.cp
    
    Triple Productsc.m.va.tp
    
    Position, Displacement and Separation Vectorsc.m.va.pds
  - Differential Calculusc.m.dc
    
    Gradientc.m.dc.g
    
    The \({\boldsymbol \nabla}\) Operatorc.m.dc.del
    
    The Divergencec.m.dc.div
    
    The Curlc.m.dc.curl
    
    Product Rulesc.m.dc.pr
    
    Second Derivativesc.m.dc.d2
  - Integral Calculusc.m.ic
    
    Line, Surface and Volume Integralsc.m.ic.lsv
    
    The Fundamental Theorem of Calculusc.m.ic.ftc
    
    The Fundamental Theorem for Gradientsc.m.ic.ftg
    
    Gauss' Theoremc.m.ic.gauss
    
    Stokes' Theoremc.m.ic.stokes
    
    Integration by Partsc.m.ic.ip
  - Coordinate Systemsc.m.cs
    
    Spherical Coordinatesc.m.cs.sph
    
    Cylindrical Coordinatesc.m.cs.cyl
    
    Hyperbolic Coordinatesc.m.cs.hyp
  - Dirac delta Distributionc.m.dd
    
    The Divergence of \(\hat{\bf r}/r^2\)c.m.dd.div
    
    The One-Dimensional Dirac Delta Functionc.m.dd.1d
    
    The Three-Dimensional Delta Functionc.m.dd.3d
  - Vector Fieldsc.m.vf
    
    The Helmholtz Theoremc.m.vf.helm
    
    Potentialsc.m.vf.pot
  - Useful Formulasc.m.uf
    
    Cylindrical coordinatesc.m.uf.cyl
    
    Spherical coordinatesc.m.uf.sph
    
    Vector identitiesc.m.uf.vi

Prev: The Three-Dimensional Delta Function [c.m.dd.3d]
Next: The Helmholtz Theorem [c.m.vf.helm]
Up: Mathematics [c.m]

Vector Fieldsc.m.vf

In this section:

The Helmholtz Theoremc.m.vf.helm
Potentialsc.m.vf.pot

Author: Jean-Sébastien Caux

Created: 2022-02-08 Tue 06:55