Table of Contents
Introduction and Survey
Maxwell Equations in Vacuum, Fields, and Sources
Inverse Square Law, or the Mass of the Photon
Linear Superposition
Maxwell Equations in Macroscopic Media
Boundary Conditions at Interfaces Between Different
Media
Some Remarks on Idealizations in Electromagnetism
Chapter 1 / Introduction to Electrostatics
Coulomb’s Law
Electric Field
Gauss’s Law
Differential Form of Gauss’s Law
Another Equation of Electrostatics and the Scalar
Potential
Surface Distributions of Charges and Dipoles and
Discontinuities in the Electric Field and Potential
Poisson and Laplace Equations
Green’s Theorem
Uniqueness of the Solution with Dirichlet or Neumann Boundary
Conditions
Formal Solution of Electrostatic Boundary-Value Problem
with Green Function
Electrostatic Potential Energy and Energy Density;
Capacitance
Problems
Chapter 2 / Boundary- Value Problems in Electrostatics:
I
Method of Images
Point Charge in the Presence of a Grounded Conducting
Sphere
Point Charge in the Presence of a Charged, Insulated,
Conducting Sphere
Point Charge Near a Conducting Sphere at Fixed
Potential
Conducting Sphere in a Uniform Electric Field by Method of
Images
Green Function for the Sphere; General Solution for the
Potential
Conducting Sphere with Hemispheres at Different
Potentials
Orthogonal Functions and Expansions
Separation of Variables; Laplace Equation in Rectangular
Coordinates
A Two-Dimensional Potential Problem; Summation of Fourier
Series
Fields and Charge Densities in Two-Dimensional Corners and
Along Edges
Introduction to Finite Element Analysis for
Electrostatics
Problems
Chapter 3 / Boundary- Value Problems in Electrostatics:
II
Laplace Equation in Spherical Coordinates
Legendre Equation and Legendre Polynomials
Boundary-Value Problems with Azimuthal Symmetry
Behavior of Fields in a Conical Hole or Near a Sharp
Point
Associated Legendre Functions and the Spherical
Harmonics
Addition Theorem for Spherical Harmonics
Laplace Equation in Cylindrical Coordinates; Bessel
Functions
Boundary-Value Problems in Cylindrical Coordinates
Expansion of Green Functions in Spherical
Coordinates
Solution of Potential Problems with the Spherical Green
Function Expansion
Problems
Chapter 4 / Multipoles, Electrostatics of Macroscopic
Media, Dielectrics
Multipole Expansion
Multipole Expansion of the Energy of a Charge Distribution in
an External Field
Elementary Treatment of Electrostatics with Ponderable
Media
Boundary-Value Problems with Dielectrics
Molecular Polarizability and Electric Susceptibility
Models for Electric Polarizability
Electrostatic Energy in Dielectric Media
Problems
Chapter 5 / Magnetostatics, Faraday’s Law, Quasi-Static
Fields
Introduction and Definitions
Biot and Savart Law
Differential Equations of Magnetostatics and Ampere’s
Law
Vector Potential
Vector Potential and Magnetic Induction for a Circular Current
Loop
Magnetic Fields of a Localized Current Distribution, Magnetic
Moment
Force and Torque on and Energy of a Localized Current
Distribution in an External Magnetic Induction
Macroscopic Equations, Boundary Conditions
on B and H
Methods of Solving Boundary-Value Problems in
Magnetostatics
Uniformly Magnetized Sphere
Magnetized Sphere in an External Field; Permanent
Magnets
Numerical Methods for Two-Dimensional Magnetic
Fields
Faraday’s Law of Induction
Energy in the Magnetic Field
Energy and Self- and Mutual Inductances
Quasi-Static Magnetic Fields in Conductors; Eddy Currents;
Magnetic Diffusion
Problems
Chapter 6 / Maxwell Equations, Conservation
Laws
Maxwell’s Displacement Current; Maxwell Equations
Vector and Scalar Potentials
Gauge Transformations, Lorenz Gauge, Coulomb Gauge
Green Functions for the Wave Equation
Retarded Solutions for the Fields: Jefimenko’s Generalizations
of the Coulomb and Biot-Savart Laws; Heaviside-Feynman Expressions
for Fields of Point Charge
Derivation of the Equations of Macroscopic
Electromagnetism
Poynting’s Theorem and Conservation of Energy and Momentum for
a System of Charged Particles and Electromagnetic Fields
Transformation Properties of Electromagnetic Fields and Sources
Under Rotations, Spatial Reflections, and Time Reversal
On the Question of Magnetic Monopoles
Discussion of the Dirac Quantization Condition
Polarization Potentials (Hertz Vectors)
Problems
Chapter 7 / Plane Electromagnetic Waves and Wave
Propagation
Plane Waves in a Nonconducting Medium
Linear and Circular Polarization; Stokes Parameters
Reflection and Refraction of Electromagnetic Waves at a Plane
Interface Between Two Dielectrics
Polarization by Reflection, Total Internal
Reflection; Goos-Hänchen Effect
Frequency Dispersion Characteristics of Dielectrics,
Conductors, and Plasmas
Simplified Model of Propagation in the Ionosphere and
Magnetosphere
Magnetohydrodynamic Waves
Superposition of Waves in One Dimension; Group
Velocity
Illustration of the Spreading of a Pulse as It Propagates
in a Dispersive Medium
Causality in the Connection
Between D and E; Kramers-Kronig Relations
Problems
Chapter 8 / Waveguides, Resonant Cavities, and Optical
Fibers
Fields at the Surface of and Within a Conductor
Cylindrical Cavities and Waveguides
Waveguides
Modes in a Rectangular Waveguide
Energy Flow and Attenuation in Waveguides
Resonant Cavities
Power Losses in a Cavity; Q of a Cavity
Earth and Ionosphere as a Resonant Cavity: Schumann
Resonances
Multimode Propagation in Optical Fibers
Modes in Dielectric Waveguides
Problems
Chapter 9 / Radiating Systems, Multipole Fields and
Radiation
Fields and Radiation of a Localized Oscillating
Source
Electric Dipole Fields and Radiation
Magnetic Dipole and Electric Quadrupole Fields
Center-Fed Linear Antenna
Spherical Wave Solutions of the Scalar Wave Equation
Multipole Expansion of the Electromagnetic Fields
Properties of Multipole Fields, Energy and Angular Momentum of
Multipole Radiation
Angular Distribution of Multipole Radiation
Sources of Multipole Radiation; Multipole Moments
Multipole Radiation from a Linear, Center-Fed
Antenna
Problems
Chapter 10 / Scattering and Diffraction
1. Scattering at
Long Wavelengths
2. Scalar
Diffraction Theory
3. Vector
Equivalents of the Kirchhoff Integral
4.
Vectorial Diffraction Theory
5.
Babinet’s Principle of Complementary Screens
6. Diffraction
by a Circular Aperture; Remarks on Small Apertures
7. Scattering in
the Short-Wavelength Limit
8. Optical
Theorem and Related Matters
Problems
Chapter 11 / Special Theory of Relativity
The Situation Before 1900, Einstein’s Two Postulates
Some Recent Experiments
Lorentz Transformations and Basic Kinematic Results of Special
Relativity
Addition of Velocities; 4-Velocity
Relativistic Momentum and Energy of a Particle
Mathematical Properties of the Space-Time of Special
Relativity
Matrix Representation of Lorentz Transformations, Infinitesimal
Generators
Thomas Precession
Invariance of Electric Charge; Covariance of
Electrodynamics
Transformation of Electromagnetic Fields
Note on Notation and Units in Relativistic
Kinematics
Problems
Chapter 12 / Dynamics of Relativistic Particles and
Electromagnetic Fields
Lagrangian and Hamiltonian for a Relativistic Charged Particle
in External Electromagnetic Fields
Motion in a Uniform, Static Magnetic Field
Motion in Combined, Uniform, Static Electric and Magnetic
Fields
Particle Drifts in Nonuniform, Static Magnetic
Fields
Lowest Order Relativistic Corrections to the Lagrangian for
Interacting Charged Particles: The Darwin Lagrangian
Lagrangian for the Electromagnetic Field
Proca Lagrangian; Photon Mass Effects
Effective “Photon” Mass in Superconductivity; London
Penetration Depth
Canonical and Symmetric Stress Tensors; Conservation
Laws
Solution of the Wave Equation in Covariant Form; Invariant
Green Functions
Problems
Chapter 13 / Collisions, Energy Loss, and Scattering of
Charged Particles, Cherenkov
and Transition Radiation
Energy Transfer in Coulomb Collision Between Heavy Incident
Particle and Free Electron; Energy Loss in Hard
Collisions
Energy Loss from Soft Collisions; Total Energy Loss
Density Effect in Collisional Energy Loss
Cherenkov Radiation
Elastic Scattering of Fast Charged Particles by
Atoms
Transition Radiation
Problems
Chapter 14 / Radiation by Moving
Charges
Lienard-Wiechert Potentials and Fields for a Point
Charge
Total Power Radiated by an Accelerated Charge: Larmor’s Formula
and Its Relativistic Generalization
Angular Distribution of Radiation Emitted by an Accelerated
Charge
Frequency Spectrum of Radiation Emitted by a Relativistic
Charged Particle in Instantaneously Circular Motion
Undulators and Wigglers for Synchrotron Light Sources
Thomson Scattering of Radiation
Problems
Chapter 15 / Bremsstrahlung, Radiative Beta
Processes
Radiation Emitted During Collisions
Bremsstrahlung in Coulomb Collisions
Screening Effects; Relativistic Radiative Energy
Loss
Radiation Emitted During Beta Decay
Problems
Chapter 16 / Radiation Damping, Classical Models of
Charged Particles
Introductory Considerations
Radiative Reaction Force from Conservation of Energy
Abraham-Lorentz Evaluation of the Self-Force
Relativistic Covariance; Stability and Poincare
Stresses
Covariant Definitions of Electromagnetic Energy and
Momentum
Covariant Stable Charged Particle
Level Breadth and Level Shift of a Radiating
Oscillator
Scattering and Absorption of Radiation by an
Oscillator
Problems
A / Appendix on Units and Dimensions
Units and Dimensions, Basic Units and Derived Units
Electromagnetic Units and Equations
Various Systems of Electromagnetic Units
Conversion of Equations and Amounts Between SI Units and
Gaussian Units
B / Appendix on Equations of Macroscopic
Electromagnetism
References and Suggested Reading
Index
