Classical Electrodynamics

Cover
Tables and Formulae—1
Vector Formulas
Theorems from Vector Calculus
Half-Title Page
Title Page
Copyright
Dedication
Preface
Preface to the Second Edition
Preface to the First Edition
Contents
Introduction and Survey
I.1 Maxwell Equations in Vacuum, Fields, and Sources
I.2 Inverse Square Law or the Mass of the Photon
I.3 Linear Superposition
I.4 Maxwell Equations in Macroscopic Media
I.5 Boundary Conditions at Interfaces Between Different Media
I.6 Some Remarks on Idealizations in Electromagnetism
References and Suggested Reading
CHAPTER 1 Introduction to Electrostatics
1.1 Coulomb's Law
1.2 Electric Field
1.3 Gauss's Law
1.4 Differential Form of Gauss's Law
1.5 Another Equation of Electrostatics and the Scalar Potential
1.6 Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential
1.7 Poisson and Laplace Equations
1.8 Green's Theorem
1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions
1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function
1.11 Electrostatic Potential Energy and Energy Density; Capacitance
1.12 Variational Approach to the Solution of the Laplace and Poisson Equations
1.13 Relaxation Method for Two-Dimensional Electrostatic Problems
References and Suggested Reading
Problems
CHAPTER 2 Boundary- Value Problems in Electrostatics: I
2.1 Method of Images
2.2 Point Charge in the Presence of a Grounded Conducting Sphere
2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere
2.4 Point Charge Near a Conducting Sphere at Fixed Potential
2.5 Conducting Sphere in a Uniform Electric Field by Method of Images
2.6 Green Function for the Sphere; General Solution for the Potential
2.7 Conducting Sphere with Hemispheres at Different Potentials
2.8 Orthogonal Functions and Expansions
2.9 Separation of Variables; Laplace Equation in Rectangular Coordinates
2.10 A Two-Dimensional Potential Problem; Summation of a Fourier Series
2.11 Fields and Charge Densities in Two-Dimensional Corners and Along Edges
2.12 Introduction to Finite Element Analysis for Electrostatics
References and Suggested Reading
Problems
CHAPTER 3 Boundary- Value Problems in Electrostatics: II
3.1 Laplace Equation in Spherical Coordinates
3.2 Legendre Equation and Legendre Polynomials
3.3 Boundary-Value Problems with Azimuthal Symmetry
3.4 Behavior of Fields in a Conical Hole or Near a Sharp Point
3.5 Associated Legendre Functions and the Spherical Harmonics $Y_{lm}(\theta, \phi)$
3.6 Addition Theorem for Spherical Harmonics
3.7 Laplace Equation in Cylindrical Coordinates; Bessel Functions
3.8 Boundary-Value Problems in Cylindrical Coordinates
3.9 Expansion of Green Functions in Spherical Coordinates
3.10 Solution of Potential Problems with the Spherical Green Function Expansion
3.11 Expansion of Green Functions in Cylindrical Coordinates
3.12 Eigenfunction Expansions for Green Functions
3.13 Mixed Boundary Conditions; Conducting Plane with a Circular Hole
References and Suggested Reading
Problems
CHAPTER 4 Multipoles, Electrostatics of Macroscopic Media, Dielectrics
4.1 Multipole Expansion
4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field
4.3 Elementary Treatment of Electrostatics with Ponderable Media
4.4 Boundary-Value Problems with Dielectrics
4.5 Molecular Polarizability and Electric Susceptibility
4.6 Models for the Molecular Polarizability
4.7 Electrostatic Energy in Dielectric Media
References and Suggested Reading
Problems
CHAPTER 5 Magnetostatics, Faraday's Law, Quasi-Static Fields
5.1 Introduction and Definitions
5.2 Biot and Savart Law
5.3 Differential Equations of Magnetostatics and Ampère's Law
5.4 Vector Potential
5.5 Vector Potential and Magnetic Induction for a Circular Current Loop
5.6 Magnetic Fields of a Localized Current Distribution, Magnetic Moment
5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction
5.8 Macroscopic Equations, Boundary Conditions on B and H
5.9 Methods of Solving Boundary- Value Problems in Magnetostatics
5.10 Uniformly Magnetized Sphere
5.11 Magnetized Sphere in an External Field; Permanent Magnets
5.12 Magnetic Shielding, Spherical Shell of Permeable Material in a Uniform Field
5.13 Effect of a Circular Hole in a Perfectly Conducting Plane with an Asymptotically Uniform Tangential Magnetic Field on One Side
5.14 Numerical Methods for Two-Dimensional Magnetic Fields
5.15 Faraday's Law of Induction
5.16 Energy in the Magnetic Field
5.17 Energy and Self- and Mutual Inductances
A. Coefficients of Self- and Mutual Inductance
B. Estimation of Self-Inductance for Simple Circuits
Exercise
5.18 Quasi-Static Magnetic Fields in Conductors; Eddy Currents; Magnetic Diffusion
A. Skin Depth, Eddy Currents, Induction Heating
B. Diffusion of Magnetic Fields in Conducting Media
References and Suggested Reading
Problems
CHAPTER 6 Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws
6.1 Maxwell's Displacement Current; Maxwell Equations
6.2 Vector and Scalar Potentials
6.3 Gauge Transformations, Lorenz Gauge, Coulomb Gauge
6.4 Green Functions for the Wave Equation
6.5 Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulomb and Biot-Savart Laws; Heaviside-Feynman Expressions for Fields of Point Charge
6.6 Derivation of the Equations of Macroscopic Electromagnetism
6.7 Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields
6.8 Poynting's Theorem in Linear Dispersive Media with Losses
6.9 Poynting's Theorem for Harmonic Fields; Field Definitions of Impedance and Admittance
6.10 Transformation Properties of Electromagnetic Fields and Sources Under Rotations, Spatial Reflections, and Time Reversal
A. Rotations
B. Spatial Reflection or Inversion
C. Time Reversal
D. Electromagnetic Quantities
6.11 On the Question of Magnetic Monopoles
6.12 Discussion of the Dirac Quantization Condition
6.13 Polarization Potentials (Hertz Vectors)
References and Suggested Reading
Problems
CHAPTER 7 Plane Electromagnetic Waves and Wave Propagation
7.1 Plane Waves in a Nonconducting Medium
7.2 Linear and Circular Polarization; Stokes Parameters
7.3 Reflection and Refraction of Electromagnetic Waves at a Plane Interface Between Dielectrics
7.4 Polarization by Reflection and Total Internal Reflection; Goos-Hanchen Effect
7.5 Frequency Dispersion Characteristics of Dielectrics, Conductors, and Plasmas
A. Simple Model for ε(ω)
B. Anomolous Dispersion and Resonant Absorption
C. Low-Frequency Behavior, Electric Conductivity
D. High-Frequency Limit, Plasma Frequency
E. Index of Refraction and Absorption Coefficient of Liquid Water as a Function of Frequency
7.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere
7.7 Magnetohydrodynamic Waves
7.8 Superposition of Waves in One Dimension; Group Velocity
7.9 Illustration of the Spreading of a Pulse as It Propagates in a Dispersive Medium
7.10 Causality in the Connection Between D and E; Kramers-Kronig Relations
A. Nonlocality in Time
B. Simple Model for G(τ), Limitations
C. Causality and Analyticity Domain of ε(ω)
D. Kramers-Kronig Relations
7.11 Arrival of a Signal After Propagation Through a Dispersive Medium
References and Suggested Reading
Problems
CHAPTER 8 Waveguides, Resonant Cavities, and Optical Fibers
8.1 Fields at the Surface of and Within a Conductor
8.2 Cylindrical Cavities and Waveguides
8.3 Waveguides
8.4 Modes in a Rectangular Waveguide
8.5 Energy Flow and Attenuation in Waveguides
8.6 Perturbation of Boundary Conditions
8.7 Resonant Cavities
8.8 Power Losses in a Cavity; Q of a Cavity
8.9 Earth and Ionosphere as a Resonant Cavity: Schumann Resonances
8.10 Multimode Propagation in Optical Fibers
8.11 Modes in Dielectric Waveguides
A. Modes in a Planar Slab Dielectric Waveguide
B. Modes in Circular Fibers
8.12 Expansion in Normal Modes; Fields Generated by a Localized Source in a Hollow Metallic Guide
A. Orthonormal Modes
B. Expansion of Arbitrary Fields
C. Fields Generated by a Localized Source
D. Obstacles in Waveguides
References and Suggested Reading
Problems
CHAPTER 9 Radiating Systems, Multipole Fields and Radiation
9.1 Fields and Radiation of a Localized Oscillating Source
9.2 Electric Dipole Fields and Radiation
9.3 Magnetic Dipole and Electric Quadrupole Fields
9.4 Center-Fed Linear Antenna
A. Approximation of Sinusoidal Current
B. The Antenna as a Boundary-Value Problem
9.5 Multipole Expansion for Localized Source or Aperture in Waveguide
A. Current Source Inside Guide
B. Aperture in Side Walls of Guide
C. Effective Dipole Moments of Apertures
9.6 Spherical Wave Solutions of the Scalar Wave Equation
9.7 Multipole Expansion of the Electromagnetic Fields
9.8 Properties of Multipole Fields; Energy and Angular Momentum of Multipole Radiation
9.9 Angular Distribution of Multipole Radiation
9.10 Sources of Multipole Radiation; Multipole Moments
9.11 Multipole Radiation in Atoms and Nuclei
9.12 Multipole Radiation from a Linear, Center-Fed Antenna
References and Suggested Reading
Problems
CHAPTER 10 Scattering and Diffraction
10.1 Scattering at Long Wavelengths
A. Scattering by Dipoles Induced in Small Scatterers
B. Scattering by a Small Dielectric Sphere
C. Scattering by a Small Perfectly Conducting Sphere
D. Collection of Scatterers
10.2 Perturbation Theory of Scattering, Rayleigh's Explanation of the Blue Sky, Scattering by Gases and Liquids, Attenuation in Optical Fibers
A. General Theory
B. Born Approximation
C. Blue Sky: Elementary Argument
D. Density Fluctuations; Critical Opalescence
E. Attenuation in Optical Fibers
10.3 Spherical Wave Expansion of a Vector Plane Wave
10.4 Scattering of Electromagnetic Waves by a Sphere
10.5 Scalar Diffraction Theory
10.6 Vector Equivalents of the Kirchhoff Integral
10.7 Vectorial Diffraction Theory
10.8 Babinet's Principle of Complementary Screens
10.9 Diffraction by a Circular Aperture; Remarks on Small Apertures
10.10 Scattering in the Short-Wavelength Limit
10.11 Optical Theorem and Related Matters
References and Suggested Reading
Problems
CHAPTER 11 Special Theory of Relativity
11.1 The Situation Before 1900, Einstein's Two Postulates
11.2 Some Recent Experiments
A. Ether Drift
B. Speed of Light from a Moving Source
C. Frequency Dependence of the Speed of Light in Vacuum
11.3 Lorentz Transformations and Basic Kinematic Results of Special Relativity
A. Simple Lorentz Transformation of Coordinates
B. 4-Vectors
C. Light Cone, Proper Time, and Time Dilation
D. Relativistic Doppler Shift
11.4 Addition of Velocities, 4-Velocity
11.5 Relativistic Momentum and Energy of a Particle
11.6 Mathematical Properties of the Space-Time of Special Relativity
11.7 Matrix Representation of Lorentz Transformations, Infinitesimal Generators
11.8 Thomas Precession
11.9 Invariance of Electric Charge; Covariance of Electrodynamics
11.10 Transformation of Electromagnetic Fields
11.11 Relativistic Equation of Motion for Spin in Uniform or Slowly Varying External Fields
A. Covariant Equation of Motion
B. Connection to the Thomas Precession
C. Rate of Change of Longitudinal Polarization
11.12 Note on Notation and Units in Relativistic Kinematics
References and Suggested Reading
Problems
CHAPTER 12 Dynamics of Relativistic Particles and Electromagnetic Fields
12.1 Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields
A. Elementary Approach to a Relativistic Lagrangian
B. Manifestly Covariant Treatment of the Relativistic Lagrangian
12.2 Motion in a Uniform, Static Magnetic Field
12.3 Motion in Combined, Uniform, Static Electric and Magnetic Fields
12.4 Particle Drifts in Nonuniform, Static Magnetic Fields
12.5 Adiabatic Invariance of Flux Through Orbit of Particle
12.6 Lowest Order Relativistic Corrections to the Lagrangian for Interacting Charge Particles: The Darwin Lagrangian
12.7 Lagrangian for the Electromagnetic Field
12.8 Proca Lagrangian; Photon Mass Effects
12.9 Effective "Photon" Mass in Superconductivity; London Penetration Depth
12.10 Canonical and Symmetric Stress Tensors; Conservation Laws
A. Generalization of the Hamiltonian: Canonical Stress Tensor
B. Symmetric Stress Tensor
C. Conservation Laws for Electromagnetic Fields Interacting with Charged Particles
12.11 Solution of the Wave Equation in Covariant Form; Invariant Green Functions
References and Suggested Reading
Problems
CHAPTER 13 Collisions, Energy Loss, and Scattering of Charged Particles; Cherenkov and Transition Radiation
13.1 Energy Transfer in a Coulomb Collision Between Heavy Incident Particle and Stationary Free Electron; Energy Loss in Hard Collisions
13.2 Energy Loss from Soft Collisions; Total Energy Loss
13.3 Density Effect in Collisional Energy Loss
13.4 Cherenkov Radiation
13.5 Elastic Scattering of Fast Charged Particles by Atoms
13.6 Mean Square Angle of Scattering; Angular Distribution of Multiple Scattering
13.7 Transition Radiation
References and Suggested Reading
Problems
CHAPTER 14 Radiation by Moving Charges
14.1 Liénard-Wiechert Potentials and Fields for a Point Charge
14.2 Total Power Radiated by an Accelerated Charge: Larmor's Formula and Its Relativistic Generalization
14.3 Angular Distribution of Radiation Emitted by an Accelerated Charge
14.4 Radiation Emitted by a Charge in Arbitrary, Extremely Relativistic Motion
14.5 Distribution in Frequency and Angle of Energy Radiated by Accelerated Charges: Basic Results
14.6 Frequency Spectrum of Radiation Emitted by a Relativistic Charged Particle in Instantaneously Circular Motion
14.7 Undulators and Wigglers for Synchrotron Light Sources
A. Qualitative Features
(a) Wiggler ($\psi_0 \gg \Delta\theta$)
(b) Undulators ($\psi_0 \ll \Delta\theta$ or $K \ll 1$)
B. Some Details of the Kinematics and Particle Dynamics
C. Particle Motion in the Average Rest Frame
D. Radiation Spectrum from an Undulator
(a) Angular Distribution
(b) Frequency Distribution
(c) Energy of Photons and Number Emitted per Magnet Period
E. Numerical Values and Representative Spectra and Facilities
F. Additional Comments
14.8 Thomson Scattering of Radiation
References and Suggested Reading
Problems
CHAPTER 15 Bremsstrahlung, Method of Virtual Quanta, Radiative Beta Processes
15.1 Radiation Emitted During Collisions
A. Low-Frequency Limit
B. Polarization and Spectrum Integrated over Angles
C. Qualitative Behavior at Finite Frequencies
15.2 Bremsstrahlung in Coulomb Collisions
A. Classical Bremsstrahlung
B. Nonrelativistic Bremsstrahlung
C. Relativistic Bremsstrahlung
D. Relativistic Bremsstrahlung by a Lorentz Transformation
15.3 Screening Effects; Relativistic Radiative Energy Loss
15.4 Weizsäcker-Williams Method of Virtual Quanta
15.5 Bremsstrahlung as the Scattering of Virtual Quanta
15.6 Radiation Emitted During Beta Decay
15.7 Radiation Emitted During Orbital-Electron Capture: Disappearance of Charge and Magnetic Moment
References and Suggested Reading
Problems
CHAPTER 16 Radiation Damping, Classical Models of Charged Particles
16.1 Introductory Considerations
16.2 Radiative Reaction Force from Conservation of Energy
16.3 Abraham-Lorentz Evaluation of the Self-Force
16.4 Relativistic Covariance; Stability and Poincare Stresses
16.5 Covariant Definitions of Electromagnetic Energy and Momentum
16.6 Covariant Stable Charged Particle
A. The Model
B. The Electromagnetic and Poincare Stress Tensors; Arbitrariness
C. The Poincaré Function t(z) and Contributions to the Mass
D. Demonstration of the Covariance of the Particle's Energy and Momentum
16.7 Line Breadth and Level Shift of a Radiating Oscillator
16.8 Scattering and Absorption of Radiation by an Oscillator
References and Suggested Reading
Problems
Appendix on Units and Dimensions
1 Units and Dimensions; Basic Units and Derived Units
2 Electromagnetic Units and Equations
3 Various Systems of Electromagnetic Units
4 Conversion of Equations and Amounts Between SI Units and Gaussian Units
Bibliography
Index
Tables and Formulae—2
Where to Find Key Material on Special Functions
Explicit Forms of Vector Operations