Classical Electrodynamics, International Adaptation

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-Hanchen 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 
4. Cherenkov Radiation 
5. Elastic Scattering of Fast Charged Particles by Atoms 
6. Transition Radiation  

Problems 

Chapter 14 / Radiation by Moving Charges  

1. Lienard-Wiechert Potentials and Fields for a Point Charge 
2. Total Power Radiated by an Accelerated Charge: Larmor’s Formula and Its Relativistic Generalization 
3. Angular Distribution of Radiation Emitted by an Accelerated Charge
4. Frequency Spectrum of Radiation Emitted by a Relativistic Charged Particle in Instantaneously Circular Motion
5. Undulators and Wigglers for Synchrotron Light Sources
6. Thomson Scattering of Radiation 

Problems 

Chapter 15 / Bremsstrahlung, Radiative Beta Processes  

1. Radiation Emitted During Collisions 
2. Bremsstrahlung in Coulomb Collisions 
3. Screening Effects; Relativistic Radiative Energy Loss 
4. Radiation Emitted During Beta Decay 

Problems 

Chapter 16 / Radiation Damping, Classical Models of Charged Particles 

1. Introductory Considerations 
2. Radiative Reaction Force from Conservation of Energy 
3. Abraham-Lorentz Evaluation of the Self-Force 
4. Relativistic Covariance; Stability and Poincare Stresses 
5. Covariant Definitions of Electromagnetic Energy and Momentum 
6. Covariant Stable Charged Particle 
7. Level Breadth and Level Shift of a Radiating Oscillator 
8. 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