Introduction and Survey

1. Maxwell Equations in Vacuum, Fields, and Sources
2. Inverse Square Law, or the Mass of the Photon
3. Linear Superposition
4. Maxwell Equations in Macroscopic Media
5. Boundary Conditions at Interfaces Between Different Media
6. Some Remarks on Idealizations in Electromagnetism

Chapter 1 / Introduction to Electrostatics

1. Coulomb's Law
2. Electric Field
3. Gauss's Law
4. Differential Form of Gauss's Law
5. Another Equation of Electrostatics and the Scalar Potential
6. Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential
7. Poisson and Laplace Equations
8. Green's Theorem
9. Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions
10. Formal Solution of Electrostatic Boundary-Value Problem with Green Function
11. Electrostatic Potential Energy and Energy Density; Capacitance

Problems

Chapter 2 / Boundary- Value Problems in Electrostatics: I

1. Method of Images
2. Point Charge in the Presence of a Grounded Conducting Sphere
3. Point Charge in the Presence of a Charged, Insulated, Conducting Sphere
4. Point Charge Near a Conducting Sphere at Fixed Potential
5. Conducting Sphere in a Uniform Electric Field by Method of Images
6. Green Function for the Sphere; General Solution for the Potential
7. Conducting Sphere with Hemispheres at Different Potentials
8. Orthogonal Functions and Expansions
9. Separation of Variables; Laplace Equation in Rectangular Coordinates
10. A Two-Dimensional Potential Problem; Summation of Fourier Series
11. Fields and Charge Densities in Two-Dimensional Corners and Along Edges
12. Introduction to Finite Element Analysis for Electrostatics

Problems

Chapter 3 / Boundary- Value Problems in Electrostatics: II

1. Laplace Equation in Spherical Coordinates
2. Legendre Equation and Legendre Polynomials
3. Boundary-Value Problems with Azimuthal Symmetry
4. Behavior of Fields in a Conical Hole or Near a Sharp Point
5. Associated Legendre Functions and the Spherical Harmonics
6. Addition Theorem for Spherical Harmonics
7. Laplace Equation in Cylindrical Coordinates; Bessel Functions
8. Boundary-Value Problems in Cylindrical Coordinates
9. Expansion of Green Functions in Spherical Coordinates
10. Solution of Potential Problems with the Spherical Green Function Expansion

Problems

Chapter 4 / Multipoles, Electrostatics of Macroscopic Media, Dielectrics

1. Multipole Expansion
2. Multipole Expansion of the Energy of a Charge Distribution in an External Field
3. Elementary Treatment of Electrostatics with Ponderable Media
4. Boundary-Value Problems with Dielectrics
5. Molecular Polarizability and Electric Susceptibility
6. Models for Electric Polarizability
7. Electrostatic Energy in Dielectric Media

Problems

Chapter 5 / Magnetostatics, Faraday's Law, Quasi-Static Fields

1. Introduction and Definitions
2. Biot and Savart Law
3. Differential Equations of Magnetostatics and Ampere's Law
4. Vector Potential
5. Vector Potential and Magnetic Induction for a Circular Current Loop
6. Magnetic Fields of a Localized Current Distribution, Magnetic Moment
7. Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction
8. Macroscopic Equations, Boundary Conditions on B and H
9. Methods of Solving Boundary-Value Problems in Magnetostatics
10. Uniformly Magnetized Sphere
11. Magnetized Sphere in an External Field; Permanent Magnets
12. Numerical Methods for Two-Dimensional Magnetic Fields
13. Faraday's Law of Induction
14. Energy in the Magnetic Field
15. Energy and Self- and Mutual Inductances
16. Quasi-Static Magnetic Fields in Conductors; Eddy Currents; Magnetic Diffusion

Problems

Chapter 6 / Maxwell Equations, Conservation Laws

1. Maxwell's Displacement Current; Maxwell Equations
2. Vector and Scalar Potentials
3. Gauge Transformations, Lorenz Gauge, Coulomb Gauge
4. Green Functions for the Wave Equation
5. Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulomb and Biot-Savart Laws; Heaviside-Feynman Expressions for Fields of Point Charge
6. Derivation of the Equations of Macroscopic Electromagnetism
7. Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields
8. Transformation Properties of Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal
9. On the Question of Magnetic Monopoles
10. Discussion of the Dirac Quantization Condition
11. Polarization Potentials (Hertz Vectors)

Problems

Chapter 7 / Plane Electromagnetic Waves and Wave Propagation

1. Plane Waves in a Nonconducting Medium
2. Linear and Circular Polarization; Stokes Parameters
3. Reflection and Refraction of Electromagnetic Waves at a Plane Interface Between Two Dielectrics
4. Polarization by Reflection, Total Internal Reflection; Goos-Hänchen Effect
5. Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas
6. Simplified Model of Propagation in the Ionosphere and Magnetosphere
7. Magnetohydrodynamic Waves
8. Superposition of Waves in One Dimension; Group Velocity
9. Illustration of the Spreading of a Pulse as It Propagates in a Dispersive Medium
10. Causality in the Connection Between D and E; Kramers-Kronig Relations

Problems

Chapter 8 / Waveguides, Resonant Cavities, and Optical Fibers

1. Fields at the Surface of and Within a Conductor
2. Cylindrical Cavities and Waveguides
3. Waveguides
4. Modes in a Rectangular Waveguide
5. Energy Flow and Attenuation in Waveguides
6. Resonant Cavities
7. Power Losses in a Cavity; Q of a Cavity
8. Earth and Ionosphere as a Resonant Cavity: Schumann Resonances
9. Multimode Propagation in Optical Fibers
10. Modes in Dielectric Waveguides

Problems

Chapter 9 / Radiating Systems, Multipole Fields and Radiation

1. Fields and Radiation of a Localized Oscillating Source
2. Electric Dipole Fields and Radiation
3. Magnetic Dipole and Electric Quadrupole Fields
4. Center-Fed Linear Antenna
5. Spherical Wave Solutions of the Scalar Wave Equation
6. Multipole Expansion of the Electromagnetic Fields
7. Properties of Multipole Fields, Energy and Angular Momentum of Multipole Radiation
8. Angular Distribution of Multipole Radiation
9. Sources of Multipole Radiation; Multipole Moments
10. 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

1. The Situation Before 1900, Einstein's Two Postulates
2. Some Recent Experiments
3. Lorentz Transformations and Basic Kinematic Results of Special Relativity
4. Addition of Velocities; 4-Velocity
5. Relativistic Momentum and Energy of a Particle
6. Mathematical Properties of the Space-Time of Special Relativity
7. Matrix Representation of Lorentz Transformations, Infinitesimal Generators
8. Thomas Precession
9. Invariance of Electric Charge; Covariance of Electrodynamics
10. Transformation of Electromagnetic Fields
11. Note on Notation and Units in Relativistic Kinematics

Problems

Chapter 12 / Dynamics of Relativistic Particles and Electromagnetic Fields

1. Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields
2. Motion in a Uniform, Static Magnetic Field
3. Motion in Combined, Uniform, Static Electric and Magnetic Fields
4. Particle Drifts in Nonuniform, Static Magnetic Fields
5. Lowest Order Relativistic Corrections to the Lagrangian for Interacting Charged Particles: The Darwin Lagrangian
6. Lagrangian for the Electromagnetic Field
7. Proca Lagrangian; Photon Mass Effects
8. Effective "Photon" Mass in Superconductivity; London Penetration Depth
9. Canonical and Symmetric Stress Tensors; Conservation Laws
10. 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

1. Energy Transfer in Coulomb Collision Between Heavy Incident Particle and Free Electron; Energy Loss in Hard Collisions
2. Energy Loss from Soft Collisions; Total Energy Loss
3. Density Effect in Collisional Energy Loss
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