Electricity & Magnetism

This classic 1953 text for advanced undergraduates has been used by generations of physics majors. Requiring only some background in general physics and calculus, it offers in-depth coverage of electricity and magnetism and features problems at the end of each chapter. Starting with an introductory chapter on electrostatics, the treatment advances to the electrostatic field of free charges; dielectric theory; electrostatic energy, force, and capacitance; electric current; and direct-current circuits. Subsequent topics include steady-state magnetism, electromagnetic induction, magnetic properties of matter, transient currents, analysis of alternating- current circuits, Maxwell's equations, and electromagnetic waves CONTENTS Preface v CHAPTER 1 ELECTROSTATICS 1 1.1 Electric Charge 1 1.2 Coulomb's Law, and Conservation of Charge 1 1.3 Charge Density 3 1.4 Electric Field 6 1.5 Electrostatic Potential 7 1.6 Potential of a Point Charge 11 1.7 Potential of a Charge Distribution 12 1.8 Convergence of Improper Integrals 13 1.9 Flux of the Electric Field. Gauss' Law 14 1.10 Computation of Electric Field by Gauss' Law 17 1.11 Lines of Force and Equipotential Surfaces 20 1.12 Conductors in Electrostatic Systems 22 1.13 The Electric Dipole 26 1.14 Expansion of the Potential of a System of Charges 28 Problems 31 CHAPTER 2 THE ELECTROSTATIC FIELD OF FREE CHARGES. . . 37 2.1 Introduction 37 2.2 Poisson's Equation in Space. Laplace's Equation 38 2.3 Boundary Conditions 41 2.4 Poisson's Equation in Less than Three Cartesian Coordinates ... 43 2.5 Electrostatic Images 45 2.6 Image Problems Involving a Spherical Conductor 48 2.7 Equipotential Surfaces in the Form of Circular Cylinders .... 52 2.8 Line Charge and Conducting Circular Cylinder 54 2.9 Two Conducting Circular Cylinders 66 Problems 59 CHAPTER 3 DIELECTRIC THEORY 63 3.1 Introduction 63 3.2 Electric Polarization 63 3.3 A One-dimensional Model, and a Mathematical Transformation . . 66 3.4 Bound Charge 68 3.5 Electric Field within a Dielectric 72 3.6 Electric Displacement 77 3.7 Electric Susceptibility and Dielectric Constant 79 3.8 Electrostatic Potential in a Dielectric System 81 3.9 Boundary Conditions on the Field Vectors 82 3.10 Boundary Conditions for the Macroscopic Electrostatic Potential . . 86 3.11 The Poisson Equation 88 3.12 The Special Case 90 3.13 Dielectric Image Theory 92 3.14 Local Field. Permanent and Induced Dipole Momenta 94 Problems 97 CHAPTER 4 ELECTROSTATIC ENERGY, FORCE, AND CAPACITANCE 102 4.1 Meaning of Energy 102 4.2 A Fundamental Expression for Energy 104 4.3 Energy of a System Containing Macroscopic Point Charges . . . 107 4.4 Energy of Elementary Particles Ill 4.5 Electrostatic Energy in Terms of Field Vectors 112 4.6 Linear Systems of Conductors 115 4.7 Energy of a Linear System of Conductors 117 4.8 Further Properties of the Coefficients of Potential, Induction, and Capacitance 120 4.9 Condensers 121 4.10 Networks of Condensers 123 4.11 Forces on Electrostatic Charge Distributions 125 4.12 Total Electrostatic Force on a System in Vacuo 128 4.13 Electrostatic Force and Torque Derived by Energy Considerations . 129 Problems 132 CHAPTER 5 ELECTRIC CURRENT 137 5.1 Electric Current and Density 137 5.2 Surface Current Density 140 5.3 Continuity 141 5.4 Conductivity 142 5.5 Joule Heat 145 5.6 The Electric Field in a System Containing Electric Current . . . 146 5.7 Potential Difference in a Nonstatic System 147 5.8 Electromotive Force 149 5.9 Two-terminal Passive Systems. D-C Resistance 152 5.10 Two-terminal Active Systems with Direct Current 154 5.11 Charge within a Conductor 155 5.12 Steady Current Flow in a Region without EMF 156 5.13 Current Flow in a Wire. Resistivity 160 5.14 Temperature Coefficient of Resistivity 162 Problems 163 CHAPTER 6 DIRECT-CURRENT CIRCUITS 169 6.1 Components 169 6.2 The Simplest Circuit. Basic Principles 172 6.3 Series and Parallel Circuits 174 6.4 Kirchhoffs Laws 177 6.5 Loop Currents 180 6.6 Superposition 182 6.7 Equivalent EMF and Internal Resistance 183 6.8 Th6venin's Theorem 186 6.9 Maximum Power Output 188 Problems 189 CHAPTER 7 STEADY-STATE MAGNETISM 197 7.1 Introduction 197 7.2 Magnetic Induction 198 7.3 Ampere's Law 202 7.4 Magnetic Field of Wire, Loop, and Solenoid 206 7.5 Vector Potential 209 7.6 Magnetic Flux 211 7.7 Ampere's Circuital Law 214 7.8 Field of a Distant Circuit. Magnetic Dipole Moment 217 7.9 The Equivalent Network. Dipole Moment of an Arbitrary Circuit . 220 7.10 Magnetic Scalar Potential 223 7.11 Differential Form of the Circuital Law 229 7.12 Force and Torque on a Current Circuit 232 7.13 Force and Couple on a Magnetic Dipole 235 Problems 238 CHAPTERS ELECTROMAGNETIC INDUCTION 246 8.1 Motional Electromotive Force 246 8.2 EMF and Magnetic Flux: Faraday's Law of Electromagnetic Induction 249 8.3 Lenz's Law 251 8.4 Self-inductance 252 8.5 Mutual Inductance 254 8.6 Inductors 257 8.7 Limit of Mutual Inductance 259 8.8 Parallel Inductors 260 8.9 Energy Transformations in Inductors. Magnetic Stored Energy . . 261 Problems 267 CHAPTER 9 MAGNETIC PROPERTIES OF MATTER 271 9.1 Macroscopic and Microscopic Analysis 271 9.2 Relative Permeability. State of Magnetization 273 9.3 Magnetizing Force 275 9.4 Terminology of Magnetism 278 9.5 Nonferromagnetic Materials 280 9.6 Ferromagnetism 281 9.7 Origins of Magnetic Susceptibility 285 9.8 Magnetic Polarization 287 9.9 Exterior Field of Magnetized Material. Magnetic Bound Charge. . 289 9.10 Internal Field of a Magnet 294 9.11 Microscopic Analysis of Magnetizing Force 303 9.12 The Magnetic Circuit 307 9.13 Force and Torque on a Magnet in Terms of Bound Charge. . . . 312 9.14 Exterior Field of a Magnet: Bound Current Densities 319 9.15 Interior Field of a Magnet in Terms of Bound Currents .... 322 9.16 Force and Torque on a Magnet in Terms of Bound Currents . . . 327 9.17 Magnetic Energy. Hysteresis Loss . . . . 329 9.18 Magnetomechanical Energy Relations 333 Problems 336 CHAPTER 10 TRANSIENT CURRENTS 342 10.1 Circuit Components 342 10.2 Circuit Theorems for Transient Conditions 344 10.3 Simple R-L Circuits 345 10.4 Simple R-C Circuits 347 10.5 Ideal L-C Circuit 350 10.6 Series L-C-R Circuit 351 10.7 Transient Balance 355 10.8 Mutual Inductance Bridge of Carey Foster 356 10.9 Moving-coil D-C Galvanometers 358 10.10 The d'Arsonval Ballistic Galvanometer 364 Problems 367 CHAPTER 11 ANALYSIS OF ALTERNATING-CURRENT CIRCUITS . . 372 11.1 Series Circuit with A-C Generator. Transient and Steady-state Currents 372 11.2 Alternating-current Characteristics of Uncoupled Linear Circuit Components 375 11.3 Power 377 11.4 Vector Representation of A-C Variables 380 11.5 Impedance Operators and Impedance Vectors 383 11.6 Admittance 386 11.7 Complex Numbers. The Exponential Function of a Complex Variable 389 11.8 Complex Circuit Analysis 392 11.9 Resonance 395 11.10 A-C Bridges without Coupling 398 11.11 Inductive Coupling in Complex Analysis. General Theorems . . . 402 11.12 Practical Circuit Components. Frequency Dependence .... 406 11.13 Transformers 410 Problems 416 CHAPTBR 12 MAXWELL'S EQUATIONS. ELECTROMAGNETIC WAVES 422 12.1 Introduction 422 12.2 Differential Form of Faraday's Law of Electromagnetic Induction. . 422 12.3 Divergence of Magnetic Induction 424 12.4 Displacement Current 425 12.5 The Maxwell Equations. The Wave Equation in Insulating Material 429 12.6 Plane Waves in Dielectric Material 431 12.7 Energy Flow. The Poynting Vector 436 12.8 Radiation of a Harmonically Oscillating Electric Dipole 442 12.9 General Boundary Conditions 451 12.10 Reflection and Transmission of a Plane Wave at a Dielectric Interface. Normal Incidence 454 12.11 Electromagnetic Potentials 458 12.12 Electric and Magnetic Fields in Small Systems 462 Problems 466 Index 471