Pre-Quantum Electrodynamics
Table of contents
Introduction
in
Preface
in.p
Tips for the reader
in.t
Contextual colors
in.t.c
Electromagnetostatics
ems
Electrostatics
ems.es
Electric Charge
ems.es.ec
Basics
ems.es.ec.b
Conservation
ems.es.ec.c
Quantization
ems.es.ec.q
Structure
ems.es.ec.s
Electric Force and Energy
ems.es.efo
Coulomb's Law
ems.es.efo.cl
Principle of Superposition
ems.es.efo.ps
Experimental Investigations
ems.es.efo.exp
Before Coulomb
Cavendish's experiment
Coulomb
Current status
Energy in Systems of Point Charges
ems.es.efo.e
Work; Pairwise Energy
Generic assembly
Crystal lattices
Electrostatic Fields
ems.es.ef
Electrostatic Field of Point Charges
ems.es.ef.pc
Electrostatic Field of Continuous Charge Distributions
ems.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 Potential
ems.es.ep
Definition
ems.es.ep.d
Field in terms of the potential
ems.es.ep.fp
Comments on the Electrostatic Potential
ems.es.ep.c
Example calculations for the potential
ems.es.ep.ex
The Poisson Equation and the Laplace Equation
ems.es.ep.PL
Electrostatic Boundary Conditions
ems.es.ep.bc
Electrostatic Energy
ems.es.e
The Energy of a Point Charge Distribution
ems.es.e.pcd
The Energy of a Continuous Charge Distribution
ems.es.e.ccd
Comments on Electrostatic Energy
ems.es.e.c
Conductors
ems.es.c
Properties
ems.es.c.p
Induced Charges
ems.es.c.ic
Surface Charge and the Force on a Conductor
ems.es.c.sc
Capacitors
ems.es.c.cap
Calculating or Approximating the Electrostatic Potential
ems.ca
Fundamental Equations for the Electrostatic Potential
ems.ca.fe
The Laplace Equation
ems.ca.fe.L
The Laplace Equation in One Dimension
The Laplace Equation in Two Dimensions
The Laplace Equation in Three Dimensions
Green's Identities
ems.ca.fe.g
Uniqueness of Solution to Poisson's Equation
ems.ca.fe.uP
The Method of Images
ems.ca.mi
Induced Surface Charges
ems.ca.mi.isc
Force and Energy
ems.ca.mi.fe
Other Image Problems
ems.ca.mi.o
Separation of Variables
ems.ca.sv
Cartesian Coordinates
ems.ca.sv.car
Cylindrical Coordinates
ems.ca.sv.cyl
Spherical Coordinates
ems.ca.sv.sph
The Multipole Expansion
ems.ca.me
Approximate Potential at Large Distance
ems.ca.me.a
Monopole and Dipole Terms
ems.ca.me.md
Higher Moments
ems.ca.me.h
The Electric Field of a Dipole
ems.ca.me.Ed
The Electric Field of a Quadrupole
ems.ca.me.Eq
Magnetostatics
ems.ms
Charges in Motion: the Lorentz Force Law
ems.ms.lf
Point Charge
ems.ms.lf.pc
Currents
ems.ms.lf.c
Steady Currents: the Biot-Savart Law
ems.ms.BS
The Magnetic Field issuing from a Steady Current
ems.ms.BS.sc
Divergence and Curl of \({\bf B}\)
ems.ms.dcB
Straight-line Currents
ems.ms.dcB.sc
Divergence and Curl of \({\bf B}\) from Biot-Savart
ems.ms.dcB.BS
The Vector Potential
ems.ms.vp
Magnetic Boundary Conditions
ems.ms.vp.mbc
Multipole Expansion of the Vector Potential
ems.ms.vp.me
Comparison of Electrostatics and Magnetostatics
ems.ms.vp.comp
The Levi-Civita Symbol
ems.ms.vp.LC
Electromagnetostatics in matter
emsm
A proper definition of "statics"
emsm.esm.s
Electrostatics in matter
emsm.esm
Polarization
emsm.esm.p
Dielectrics
emsm.esm.d
The Field of a Polarized Object
emsm.esm.fpo
Physical Interpretation of Bound Charges
emsm.esm.fpo.pibc
The Field Inside a Dielectric
emsm.esm.fpo.fid
The Electric Displacement
emsm.esm.D
Boundary Conditions
emsm.esm.D.bc
Dielectrics
emsm.esm.di
Linear Dielectrics
emsm.esm.di.ld
Susceptibility, Permittivity, Dielectric Constant
Boundary Value Problems with Linear Dielectrics
Energy in Dielectric Systems
Forces on Dielectrics
Magnetostatics in matter
emsm.msm
Magnetization
emsm.msm.m
Diamagnetism, Paramagnetism, Ferromagnetism
emsm.msm.m.dpf
Why is Ferromagnetism such an intriguing phenomenon?
Torques and Forces on Magnetic Dipoles
emsm.msm.m.fdi
Effect of Magnetic Field on Atomic Orbits
emsm.msm.a
The Field of a Magnetized Object
emsm.msm.fmo
Bound Currents
emsm.msm.fmo.bc
Physical Interpretation of Bound Currents
emsm.msm.fmo.pibc
The Magnetic Field Inside Matter
emsm.msm.fmo.fim
The H Field
emsm.msm.H
Ampère's Law in Magnetized Materials
emsm.msm.H.A
A Deceptive Parallel
Energy in Linear Media
Linear and Nonlinear Media
emsm.msm.lnlm
Magnetic Susceptibility and Permeability
emsm.msm.lnlm.sp
Ferromagnetism
emsm.msm.lnlm.fm
Electromagnetodynamics
emd
Induction: Faraday's Law
emd.Fl
Faraday's Law
emd.Fl.Fl
The Induced Electric Field
emd.Fl.ief
Inductance
emd.Fl.i
Energy in Magnetic Fields
emd.Fl.e
Maxwell's Equations
emd.Me
Electrodynamics Before Maxwell
emd.Me.ebM
Maxwell's Correction to Ampère's Law; the Displacement Current
emd.Me.dc
Maxwell's Equations
emd.Me.Me
Magnetic Charge
emd.Me.mc
Charge and Energy Flows
emd.ce
The Continuity Equation
emd.ce.ce
Poynting's Theorem; the Poynting Vector
emd.ce.poy
Maxwell's Stress Tensor
emd.ce.mst
Momentum
emd.ce.mom
Angular Momentum
emd.ce.amom
Electromagnetic waves in vacuum
emd.emw
The Wave Equation
emd.emw.we
Monochromatic Plane Waves
emd.emw.mpw
Energy and Momentum
emd.emw.ep
Electromagnetodynamics in Matter
emdm
Maxwell's Equations in Matter
emdm.Me
Maxwell's Equations in Matter
emdm.Me.Mem
Boundary Conditions
emdm.Me.bc
Electromagnetic Waves in Matter
emdm.emwm
Propagation in Linear Media
emdm.emwm.plm
Refraction
emdm.emwm.refr
Reflection and Transmission
emdm.emwm.refl
Normal Incidence
emdm.emwm.refl.ni
Oblique Incidence
emdm.emwm.refl.oi
Fresnel's Equations
emdm.emwm.refl.Fe
Brewster's Angle
emdm.emwm.refl.Ba
Absorption and Dispersion
emdm.emwm.ad
EM Waves in Conductors
emdm.emwm.ad.c
Waveguides
emdm.emwm.wg
Guided waves
emdm.emwm.wg.gw
Rectangular Waveguides
emdm.emwm.wg.r
Coaxial Lines
emdm.emwm.wg.c
Electromagnetic Fields
emf
Scalar and Vector Potentials
emf.svp
Gauge Freedom and Choices
emf.g
Coulomb Gauge
emf.g.Cg
Lorenz Gauge; d'Alembertian; Inhomogeneous Maxwell Equations
emf.g.Lg
Relativistic Electrodynamics
red
Special Relativity
red.sr
Postulates and their consequences
red.sr.p
Lorentz Transformations
red.sr.Lt
Covariant and Contravariant Four-Vectors
red.sr.4v
Relativistic Mechanics
red.rm
Proper Time and Proper Velocity
red.rm.pt
Relativistic Momentum and Energy
red.rm.rme
Relativistic version of Newton's Laws; the Minkowski Force
red.rm.Mf
Relativistic Electromagnetism
red.rem
Magnetism as a Relativistic Effect
red.rem.mre
Lorentz Transformation of Electromagnetic Fields
red.rem.Ltf
The Field Tensor
red.rem.Fmunu
Maxwell's Equations in Relativistic Notation
red.rem.Me
Quantum Electrodynamics
qed
QED today
qed.t
Diagnostics
d
Diagnostics: Mathematical Preliminaries
d.m
Diagnostics: Electromagnetostatics
d.ems
Diagnostics: Calculating or Approximating the Electostatic Potential
d.ems.ca
Diagnostics: Electromagnetostatics in Matter
d.emsm
Diagnostics: Magnetostatics
d.ems.ms
Diagnostics: Magnetostatics in Matter
d.emsm.msm
Diagnostics: Electromagnetodynamics
d.emd
Diagnostics: Conservation Laws
d.emd.ce
Diagnostics: Electromagnetic Waves
d.emd.emw
Diagnostics: Potentials, Gauges and Fields
d.emf
Diagnostics: Relativistic Electrodynamics
d.red
Appendices
a
Literature
a.l
Compendium
c
Mathematics
c.m
Vector Analysis
c.m.va
Notation and algebraic properties
c.m.va.n
Scalar product
c.m.va.sp
Cross product
c.m.va.cp
Triple Products
c.m.va.tp
Position, Displacement and Separation Vectors
c.m.va.pds
Differential Calculus
c.m.dc
Gradient
c.m.dc.g
The \({\boldsymbol \nabla}\) Operator
c.m.dc.del
The Divergence
c.m.dc.div
The Curl
c.m.dc.curl
Product Rules
c.m.dc.pr
Second Derivatives
c.m.dc.d2
Divergence of gradient
Curl of a gradient
Gradient of the divergence
Divergence of a curl
Curl of curl
Integral Calculus
c.m.ic
Line, Surface and Volume Integrals
c.m.ic.lsv
Line Integrals
Surface Integrals
Volume Integrals
The Fundamental Theorem of Calculus
c.m.ic.ftc
The Fundamental Theorem for Gradients
c.m.ic.ftg
Gauss' Theorem
c.m.ic.gauss
Stokes' Theorem
c.m.ic.stokes
Integration by Parts
c.m.ic.ip
Coordinate Systems
c.m.cs
Spherical Coordinates
c.m.cs.sph
Gradient
Divergence
Curl
Laplacian
Cylindrical Coordinates
c.m.cs.cyl
Gradient
Divergence
Curl
Laplacian
Hyperbolic Coordinates
c.m.cs.hyp
Dirac delta Distribution
c.m.dd
The Divergence of \(\hat{\bf r}/r^2\)
c.m.dd.div
The One-Dimensional Dirac Delta Function
c.m.dd.1d
The Three-Dimensional Delta Function
c.m.dd.3d
Vector Fields
c.m.vf
The Helmholtz Theorem
c.m.vf.helm
Potentials
c.m.vf.pot
Theorem 1: Curl-less (irrotational) fields
Theorem 2: Divergence-less (solenoidal) fields
Useful Formulas
c.m.uf
Cylindrical coordinates
c.m.uf.cyl
Spherical coordinates
c.m.uf.sph
Vector identities
c.m.uf.vi
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Electromagnetodynamics in Matter
[emdm]
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Maxwell's Equations in Matter
[emdm.Me.Mem]
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Electromagnetodynamics in Matter
[emdm]
Maxwell's Equations in Matter
emdm.Me
In this section:
Maxwell's Equations in Matter
emdm.Me.Mem
Boundary Conditions
emdm.Me.bc
Author: Jean-Sébastien Caux
Created: 2022-02-07 Mon 08:02
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