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
    
    Before Coulomb
    
    Cavendish's experiment
    
    Coulomb
    
    Current status
    
    Energy in Systems of Point Chargesems.es.efo.e
    
    Work; Pairwise Energy
    
    Generic assembly
    
    Crystal lattices
  - 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
    
    Field Lines, Flux and Gauss's Law
    
    Examples of applications of Gauss's law
  - 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 Energyems.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
    
    The Laplace Equation in One Dimension
    
    The Laplace Equation in Two Dimensions
    
    The Laplace Equation in Three Dimensions
    
    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
    
    Susceptibility, Permittivity, Dielectric Constant
    
    Boundary Value Problems with Linear Dielectrics
    
    Energy in Dielectric Systems
    
    Forces on Dielectrics
- Magnetostatics in matteremsm.msm
  - Magnetizationemsm.msm.m
    
    Diamagnetism, Paramagnetism, Ferromagnetismemsm.msm.m.dpf
    
    Why is Ferromagnetism such an intriguing phenomenon?
    
    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
    
    A Deceptive Parallel
    
    Energy in Linear Media
  - 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
    
    Divergence of gradient
    
    Curl of a gradient
    
    Gradient of the divergence
    
    Divergence of a curl
    
    Curl of curl
  - Integral Calculusc.m.ic
    
    Line, Surface and Volume Integralsc.m.ic.lsv
    
    Line Integrals
    
    Surface Integrals
    
    Volume Integrals
    
    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
    
    Gradient
    
    Divergence
    
    Curl
    
    Laplacian
    
    Cylindrical Coordinatesc.m.cs.cyl
    
    Gradient
    
    Divergence
    
    Curl
    
    Laplacian
    
    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
    
    Theorem 1: Curl-less (irrotational) fields
    
    Theorem 2: Divergence-less (solenoidal) fields
  - Useful Formulasc.m.uf
    
    Cylindrical coordinatesc.m.uf.cyl
    
    Spherical coordinatesc.m.uf.sph
    
    Vector identitiesc.m.uf.vi

Prev: Theorem 2: Divergence-less (solenoidal) fields [c.m.vf.pot.solen]
Next: Cylindrical coordinates [c.m.uf.cyl]
Up: Mathematics [c.m]

Useful Formulasc.m.uf

In this section:

Cylindrical coordinatesc.m.uf.cyl
Spherical coordinatesc.m.uf.sph
Vector identitiesc.m.uf.vi

Author: Jean-Sébastien Caux

Created: 2022-02-07 Mon 08:02