Classical Electrodynamics, 3rd edition

A revision of the defining book covering the physics and classical mathematics necessary to understand electromagnetic fields in materials and at surfaces and interfaces. The third edition has been revised to address the changes in emphasis and applications that have occurred in the past twenty years. New to This Edition \*SI units used in the first 10 chapters. Gaussian units are retained in the later chapters. \*Over 110 new problems. \*New sections on the principles of numerical techniques for electrostatics and magnetostatics, as well as some elementary problems. \*Faraday’s Law and quasi-static fields are now in Chapter 5 with magnetostatics, permitting a more logical discussion of energy and inductances. \*Discussion of radiation by charge-current sources, in both elementary and exact multipole forms, has been consolidated in Chapter 9. \*Applications to scattering and diffraction are now in Chapter 10. \*Two new sections in Chapter 8 discuss the principles of optical fibers and dielectric waveguides. \*The treatment of energy loss (Chapter 13) has been shortened and strengthened. \*The discussion of synchrotron radiation as a research tool in Chapter 14 has been augmented by a detailed section on the physics of wigglers and undulators for synchrotron light sources. \*New material in Chapter 16 on radiation reaction and models of classical charged particles. 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

A revision of the defining book covering the physics and classical mathematics necessary to understand electromagnetic fields in materials and at surfaces and interfaces. The third edition has been revised to address the changes in emphasis and applications that have occurred in the past twenty years.

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A textbook for a two-semester beginning graduate course for students who have completed a standard undergraduate program for physics majors. Emphasizes the unity of electric and magnetic phenomena both in their physical basis and the mode of their mathematical description, develops and utilizes a number of tools in mathematical physics, and presents now material on the interaction of relativistic charged particles with electromagnetic fields and other areas. First published in 1962, and again in 1974; the third edition incorporates the slight drifts in emphasis and application the long-established subject has taken over the past couple of decades. Annotation c. by Book News, Inc., Portland, Or.