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This well-known undergraduate electrodynamics textbook is now available in a more affordable printing from Cambridge University Press. The Fourth Edition provides a rigorous, yet clear and accessible treatment of the fundamentals of electromagnetic theory and offers a sound platform for explorations of related applications (AC circuits, antennas, transmission lines, plasmas, optics and more). Written keeping in mind the conceptual hurdles typically faced by undergraduate students, this textbook illustrates the theoretical steps with well-chosen examples and careful illustrations. It balances text and equations, allowing the physics to shine through without compromising the rigour of the math, and includes numerous problems, varying from straightforward to elaborate, so that students can be assigned some problems to build their confidence and others to stretch their minds. A Solutions Manual is available to instructors teaching from the book; access can be requested from the resources section at www.cambridge.org/electrodynamics. Contents Preface Advertisement 1 Vector Analysis 1.1 Vector Algebra 1.1.1 Vector Operations 1.1.2 Vector Algebra: Component Form 1.1.3 Triple Products 1.1.4 Position, Displacement, and Separation Vectors 1.1.5 How Vectors Transform 1.2 Differential Calculus 1.2.1 “Ordinary” Derivatives 1.2.2 Gradient 1.2.3 The Del Operator 1.2.4 The Divergence 1.2.5 The Curl 1.2.6 Product Rules 1.2.7 Second Derivatives 1.3 Integral Calculus 1.3.1 Line, Surface, and Volume Integrals 1.3.2 The Fundamental Theorem of Calculus 1.3.3 The Fundamental Theorem for Gradients 1.3.4 The Fundamental Theorem for Divergences 1.3.5 The Fundamental Theorem for Curls 1.3.6 Integration by Parts 1.4 Curvilinear Coordinates 1.4.1 Spherical Coordinates 1.4.2 Cylindrical Coordinates 1.5 The Dirac Delta Function 1.5.1 The Divergence of ˆr/r2 1.5.2 The One-Dimensional Dirac Delta Function 1.5.3 The Three-Dimensional Delta Function 1.6 The Theory of Vector Fields 1.6.1 The Helmholtz Theorem 1.6.2 Potentials 2 Electrostatics 2.1 The Electric Field 2.1.1 Introduction 2.1.2 Coulomb’s Law 2.1.3 The Electric Field 2.1.4 Continuous Charge Distributions 2.2 Divergence and Curl of Electrostatic Fields 2.2.1 Field Lines, Flux, and Gauss’s Law 2.2.2 The Divergence of E 2.2.3 Applications of Gauss’s Law 2.2.4 The Curl of E 2.3 Electric Potential 2.3.1 Introduction to Potential 2.3.2 Comments on Potential 2.3.3 Poisson’s Equation and Laplace’s Equation 2.3.4 The Potential of a Localized Charge Distribution 2.3.5 Boundary Conditions 2.4 Work and Energy in Electrostatics 2.4.1 The Work It Takes to Move a Charge 2.4.2 The Energy of a Point Charge Distribution 2.4.3 The Energy of a Continuous Charge Distribution 2.4.4 Comments on Electrostatic Energy 2.5 Conductors 2.5.1 Basic Properties 2.5.2 Induced Charges 2.5.3 Surface Charge and the Force on a Conductor 2.5.4 Capacitors 3 Potentials 3.1 Laplace’s Equation 3.1.1 Introduction 3.1.2 Laplace’s Equation in One Dimension 3.1.3 Laplace’s Equation in Two Dimensions 3.1.4 Laplace’s Equation in Three Dimensions 3.1.5 Boundary Conditions and Uniqueness Theorems 3.1.6 Conductors and the Second Uniqueness Theorem 3.2 The Method of Images 3.2.1 The Classic Image Problem 3.2.2 Induced Surface Charge 3.2.3 Force and Energy 3.2.4 Other Image Problems 3.3 Separation of Variables 3.3.1 Cartesian Coordinates 3.3.2 Spherical Coordinates 3.4 Multipole Expansion 3.4.1 Approximate Potentials at Large Distances 3.4.2 The Monopole and Dipole Terms 3.4.3 Origin of Coordinates in Multipole Expansions 3.4.4 The Electric Field of a Dipole 4 Electric Fields in Matter 4.1 Polarization 4.1.1 Dielectrics 4.1.2 Induced Dipoles 4.1.3 Alignment of Polar Molecules 4.1.4 Polarization 4.2 The Field of a Polarized Object 4.2.1 Bound Charges 4.2.2 Physical Interpretation of Bound Charges 4.2.3 The Field Inside a Dielectric 4.3 The Electric Displacement 4.3.1 Gauss’s Law in the Presence of Dielectrics 4.3.2 A Deceptive Parallel 4.3.3 Boundary Conditions 4.4 Linear Dielectrics 4.4.1 Susceptibility, Permittivity, Dielectric Constant 4.4.2 Boundary Value Problems with Linear Dielectrics 4.4.3 Energy in Dielectric Systems 4.4.4 Forces on Dielectrics 5 Magnetostatics 5.1 The Lorentz Force Law 5.1.1 Magnetic Fields 5.1.2 Magnetic Forces 5.1.3 Currents 5.2 The Biot-Savart Law 5.2.1 Steady Currents 5.2.2 The Magnetic Field of a Steady Current 5.3 The Divergence and Curl of B 5.3.1 Straight-Line Currents 5.3.2 The Divergence and Curl of B 5.3.3 Ampère’s Law 5.3.4 Comparison of Magnetostatics and Electrostatics 5.4 Magnetic Vector Potential 5.4.1 The Vector Potential 5.4.2 Boundary Conditions 5.4.3 Multipole Expansion of the Vector Potential 6 Magnetic Fields in Matter 6.1 Magnetization 6.1.1 Diamagnets, Paramagnets, Ferromagnets 6.1.2 Torques and Forces on Magnetic Dipoles 6.1.3 Effect of a Magnetic Field on Atomic Orbits 6.1.4 Magnetization 6.2 The Field of a Magnetized Object 6.2.1 Bound Currents 6.2.2 Physical Interpretation of Bound Currents 6.2.3 The Magnetic Field Inside Matter 6.3 The Auxiliary Field H 6.3.1 Ampère’s Law in Magnetized Materials 6.3.2 A Deceptive Parallel 6.3.3 Boundary Conditions 6.4 Linear and Nonlinear Media 6.4.1 Magnetic Susceptibility and Permeability 6.4.2 Ferromagnetism 7 Electrodynamics 7.1 Electromotive Force 7.1.1 Ohm’s Law 7.1.2 Electromotive Force 7.1.3 Motional emf 7.2 Electromagnetic Induction 7.2.1 Faraday’s Law 7.2.2 The Induced Electric Field 7.2.3 Inductance 7.2.4 Energy in Magnetic Fields 7.3 Maxwell’s Equations 7.3.1 Electrodynamics Before Maxwell 7.3.2 How Maxwell Fixed Ampère’s Law 7.3.3 Maxwell’s Equations 7.3.4 Magnetic Charge 7.3.5 Maxwell’s Equations in Matter 7.3.6 Boundary Conditions 8 Conservation Laws 8.1 Charge and Energy 8.1.1 The Continuity Equation 8.1.2 Poynting’s Theorem 8.2 Momentum 8.2.1 Newton’s Third Law in Electrodynamics 8.2.2 Maxwell’s Stress Tensor 8.2.3 Conservation of Momentum 8.2.4 Angular Momentum 8.3 Magnetic Forces Do No Work 9 Electromagnetic Waves 9.1 Waves in One Dimension 9.1.1 The Wave Equation 9.1.2 Sinusoidal Waves 9.1.3 Boundary Conditions: Reflection and Transmission 9.1.4 Polarization 9.2 Electromagnetic Waves in Vacuum 9.2.1 The Wave Equation for E and B 9.2.2 Monochromatic Plane Waves 9.2.3 Energy and Momentum in Electromagnetic Waves 9.3 Electromagnetic Waves in Matter 9.3.1 Propagation in Linear Media 9.3.2 Reflection and Transmission at Normal Incidence 9.3.3 Reflection and Transmission at Oblique Incidence 9.4 Absorption and Dispersion 9.4.1 Electromagnetic Waves in Conductors 9.4.2 Reflection at a Conducting Surface 9.4.3 The Frequency Dependence of Permittivity 9.5 Guided Waves 9.5.1 Wave Guides 9.5.2 TE Waves in a Rectangular Wave Guide 9.5.3 The Coaxial Transmission Line 10 Potentials and Fields 10.1 The Potential Formulation 10.1.1 Scalar and Vector Potentials 10.1.2 Gauge Transformations 10.1.3 Coulomb Gauge and Lorenz Gauge 10.1.4 Lorentz Force Law in Potential Form 10.2 Continuous Distributions 10.2.1 Retarded Potentials 10.2.2 Jefimenko’s Equations 10.3 Point Charges 10.3.1 Liénard-Wiechert Potentials 10.3.2 The Fields of a Moving Point Charge 11 Radiation 11.1 Dipole Radiation 11.1.1 What is Radiation? 11.1.2 Electric Dipole Radiation 11.1.3 Magnetic Dipole Radiation 11.1.4 Radiation from an Arbitrary Source 11.2 Point Charges 11.2.1 Power Radiated by a Point Charge 11.2.2 Radiation Reaction 11.2.3 The Mechanism Responsible for the Radiation Reaction 12 Electrodynamics and Relativity 12.1 The Special Theory of Relativity 12.1.1 Einstein’s Postulates 12.1.2 The Geometry of Relativity 12.1.3 The Lorentz Transformations 12.1.4 The Structure of Spacetime 12.2 Relativistic Mechanics 12.2.1 Proper Time and Proper Velocity 12.2.2 Relativistic Energy and Momentum 12.2.3 Relativistic Kinematics 12.2.4 Relativistic Dynamics 12.3 Relativistic Electrodynamics 12.3.1 Magnetism as a Relativistic Phenomenon 12.3.2 How the Fields Transform 12.3.3 The Field Tensor 12.3.4 Electrodynamics in Tensor Notation 12.3.5 Relativistic Potentials A Vector Calculus in Curvilinear Coordinates A.1 Introduction A.2 Notation A.3 Gradient A.4 Divergence A.5 Curl A.6 Laplacian B The Helmholtz Theorem C Units Index What Is Electrodynamics, And How Does It Fit Into The General Scheme Of Physics? Four Realms Of Mechanics In The Diagram Below, I Have Sketched Out The Four Great Realms Of Mechanics: Classical Mechanics Quantum Mechanics (newton) (bohr, Heisenberg, Schrödinger, Et Al.) Special Relativity Quantum Field Theory (einstein) (dirac, Pauli, Feynman, Schwinger, Et Al.) Newtonian Mechanics Is Adequate For Most Purposes In Everyday Life, But For Objects Moving At High Speeds (near The Speed Of Light) It Is Incorrect, And Must Be Replaced By Special Relativity (introduced By Einstein In 1905); For Objects That Are Extremely Small (near The Size Of Atoms) It Fails For Different Reasons, And Is Superseded By Quantum Mechanics (developed By Bohr, Schrödinger, Heisenberg, And Many Others, In The 1920's, Mostly). For Objects That Are Both Very Fast And Very Small (as Is Common In Modern Particle Physics), A Mechanics That Combines Relativity And Quantum Principles Is In Order; This Relativistic Quantum Mechanics Is Known As Quantum Field Theory--it Was Worked Out In The Thirties And Forties, But Even Today It Cannot Claim To Be A Completely Satisfactory System. In This Book, Save For The Last Chapter, We Shall Work Exclusively In The Domain Of Classical Mechanics, Although Electrodynamics Extends With Unique Simplicity To The Other Three Realms. (in Fact, The Theory Is In Most Respects Automatically Consistent With Special Relativity, For Which It Was, Historically, The Main Stimulus.)-- "This well-known undergraduate electrodynamics textbook [previously published by Pearson in 2013] is now available in a more affordable printing from Cambridge University Press. The Fourth Edition provides a rigorous, yet clear and accessible treatment of the fundamentals of electromagnetic theory and offers a sound platform for explorations of related applications (AC circuits, antennas, transmission lines, plasmas, optics and more). Written keeping in mind the conceptual hurdles typically faced by undergraduate students, this textbook illustrates the theoretical steps with well-chosen examples and careful illustrations. It balances text and equations, allowing the physics to shine through without compromising the rigour of the math, and includes numerous problems, varying from straightforward to elaborate, so that students can be assigned some problems to build their confidence and others to stretch their minds"-- Publisher's description A re-issued and affordable edition of the well-known undergraduate electrodynamics textbook. The Fourth Edition provides a rigorous, yet clear and accessible treatment of the fundamentals of electromagnetic theory and offers a sound platform for explorations of related applications (AC circuits, transmission lines, plasmas, optics and more).