Table of Contents

Preface Introduction 0 Mathematical and Physical Preliminaries 0-1 "Scalars, Vectors, and Vector Algebra" 0-2 The Representation of Fields 0-3 Static Force Fields 0-4 Coordinate-Free Definitions for the Gradient and the Curl 1 Charge and Current: From Qualitative Recognition to Quantitative Measurement 1-1 The Phenomenon of Electric Charge 1-2 The Interaction of Point Charges 1-3 The Phenomenon of Current 1-4 The Interaction of Parallel Currents 1-5 Current as Charge in Motion 1-6 Units in Electricity and Magnetism 2 Charge and Current: The Specification of Arbitrary Distributions 2-1 Charge Density 2-2 Current Density 2-3 Mathematical Digression I: Strokes' Theorem and The Divergence Theorem 2-4 The Equation of Continuity 2-5 Mathematical Digression II: Several Operators Involving ? 3 The Electromagnetic Field: Its Definition and Its Effect on General Charge Distributions 3-1 Forces on Point Charges: A Definition of the Electromagnetic Field 3-2 Trajectories of Particles in Prescribed Fields 3-3 Forces and Torques on General Distributions in Prescribed Fields 4 The Electric Field Produced by Static Charges 4-1 Coulomb's Law and the Electrostatic Field of Given Sources 4-2 Gauss's Law 4-3 The Restricted Faraday Law 4-4 The Electrostatic Potential 4-5 Energy in the Electrostatic Field 4-6 The Multipole Expansion of the Electrostatic Potential 5 The Magnetic Induction Field Produced by Steady Currents 5-1 The Law of Biot-Savart 5-2 The Magnetic Flux Law 5-3 Ampere's Circutal Law 5-4 The Magnetic Vector Potential 5-5 Energy in the Static Magnetic Induction Field 5-6 The Multipole Expansion of the Magnetic Vector Potential 6 The Electromagnetic Field Produced by Time-Dependent Charge Distributions: Maxwell's Equations in Vacuum 6-1 Electromagnetic Induction: Faraday's Law 6-2 A Contradiction and its Resolution: Displacement Current 6-3 Maxwell's Equations 6-4 Energy in the Electromagnetic Field 6-5 Momentum in the Electromagnetic Field 6-6 A Reformulation Maxwell's Equations for the Potentials 6-7 Another Reformation: Decoupling the Equations for the Fields Interlude: A Change of View 7 Plane Electromagnetic Waves in Vacuum 7-1 Elementary Fields Depending on z and t; Plane Electromagnetic Waves 7-2 Energy and Momentum in Plane Waves 7-3 Superposition of Waves of the Same Frequency : Polarization and Interference 7-4 Superposition of Waves of Different Frequencies: Spectral Decomposition 7-5 Plane Waves in Three Dimensions 8 Potential Theory 8-1 Boundary Conditions 8-2 Superposition and Uniqueness 8-3 One-Dimensional Problems 8-4 Two-Dimensional Problems by Separation of Variables 8-5 Two-Dimensional Problems Using Complex Variables 8-6 The Method of Images 8-7 Numerical Solution of Laplace's Equation 8-8 Solution of Laplace's Equation by Experiment: The Method of Analogy 8-9 Poisson's Equation 9 Properties of Matter I: Conduction 9-1 Macroscopic Description: Conductivity and Ohm's Law 9-2 Microscopic Description: Carrier Mobility and Collision Times 10 Properties of Matter II: Dielectric Polarization 10-1 The Microscopic Description: Electric Polarizability 10-2 The Macroscopic Description: Dielectric Polarization 10-3 The Macroscopic Scalar Potential and Electric Field at a Point Exterior to a Polarized Dielectric 10-4 The Macroscopic Electric Field at a Point Interior to a Polarized Dielectric 10-5 The Basic Equations of Electrostatics when Dielectrics are Present 10-6 Connecting the Microscopic Polarizability with the Macroscopic Dielectric Constant: The Clausius-Mossotti Relation 11 Properties of Matter III: Magnetization 11-1 The Microscopic Description: Magnetic Polarizability 11-2 The Macroscopic Description: Magnetization 11-3 The Macroscopic Vector Potential and Magnetic Induction Field at a Point Exterior to a Magnetized Object; Bound Currents 11-4 An Alternative Approach to the Exterior Field: Equivalent Poles 11-5 The Macroscopic Magnetic Induction Field at a Point Interior to a Magnetized Object 11-6 The Basic Equations of Magnetostatics when Magnetically Responsive Matter is Present 11-7 Connecting the Microscopic Polarizability with the Macroscopic Relative Permeability 11-8 Ferromagnetism 12 Time-Dependent Fields When Matter is Present: Maxwell's Equations Revised 12-1 Maxwell's Equations in Matter 12-2 The Equation of Continuity 12-3 The Energy Theorem 12-4 The Momentum Theorem 12-5 On Which Fields are Basic 12-6 The Potentials 12-7 Boundary Conditions at Discontinuities in the Medium 12-8 Static Potentials 13 Plane Electromagnetic Waves in Linear Matter 13-1 Maxwell's Equations for Monochromatic Fields in Linear Matter 13-2 Boundary Conditions on Monochromatic Fields 13-3 "Plane Monochromatic Waves in Unbounded, Isotropic, Homogeneous, Linear Media" 13-4 Transmission and Reflection at Plane Interfaces 13-5 Wave Guides and Cavity Resonators 13-6 Superposition of Waves of Different Frequency: Dispersion 14 Radiation from Prescribed Sources in Vacuum 14-1 The General Solution of the Inhomogeneous Wave Equation; Retardation 14-2 Radiation from Monochromatic Sources: The Oscillating Electric Dipole 14-3 The Lienard-Wiechert Potentials 14-4 The Fields of a Moving Point Charge 14-5 Radiation from Accelerated Point Charges 14-6 The Radiation Reaction 15 Relativistic Formulation of Maxwell's Equations 15-1 A Review of Special Relativity 15-2 Maxwell's Equations in Covariant Form; The Electromagnetic Field Tensor 15-3 Transformation of the Electromagnetic Field 15-4 The Stress-Energy-Momentum Tensor 15-5 A New Viewpoint: The Law of Biot-Savart Revisited Appendices "A Linear Equations, Determinants, and Matrices" A-1 Simultaneous Linear Equations and Determinants A-2 Matrix Algebra B Binomial and Taylor Expansions C Vector Identities and Relationships D Complex Numbers and Fourier Analysis D-1 The Algebra of Complex Numbers D-2 Fourier Series D-3 Fourier Transforms E Reference Tables Answers to Selected Problems Index