ELECTROMAGNETIC FIELDS AND RELATIVISTIC PARTICLES Emil J. Konopinski Professor of Physics Indiana University McGraw-Hill Book Company New York St. Louis San Francisco Auckland Bogota Hamburg Johannesburg London Madrid Mexico Montreal New Delhi Panama Paris Sao Paulo Singapore Sydney Tokyo Toronto
CONTENTS Preface Introduction xi l Chapter 1 The Maxwell Equations 7 1.1 Electric Charge 1.2 Magnetism 1.3 Induction Processes Exercises Chapter 2 The Electrostatic Field 29 2.1 Superpositions of Coulomb Forces 29 2.2 The Electrostatic Potential 31 2.3 Static Multipoles 34 2.4 Electrostatic Forces and Energies 39 Exercises 50 Chapter 3 Laplace Fields 54 3.1 General Forms for the Potential,. 3.2 Fourier Analysis 3.3 Spherical Representations Exercises Chapter 4 The Magnetostatic Field 86 4.1 The Generation of Magnetostatic Fields by Currents 86 4.2 The Magnetic Dipole Approximation 94 4.3 Magnetic Forces 101 4.4 Magnetostatic Energy 110 Exercises 117 54
VI CONTENTS Chapter 5 Nonrelativistic Motions in Static Fields 122 5.1 A Point Charge in a Uniform Magnetic Field 124 5.2 The E x B Drift 126 5.3 Magnetic Dipoles in Magnetic Fields 129 5.4 The Magnetic Mirror Effect 135 5.5 The Rotation of Dipoles 139 Exercises 147 Chapter 6 Describing the General Electromagnetic Field 153 6.1 Field Energy and Its Flux 153 6.2 Field Momentum and Stress 156 6.3 Field Angular Momentum 168 6.4 Nonstatic Potentials 170 Exercises 178 Chapter 7 Plane Electromagnetic Waves 180 7.1 Wave Fields in Free Space 180 7.2 Plane Monochromatic Waves 186 ' 7.3 Wave Fields within Perfectly Reflecting Boundaries 192 Exercises 204 Chapter 8 The Generation of Electromagnetic Waves 208 8.1 Retarded Potentials 208 8.2 Radiation from Monochromatic Sources 213 8.3 Field Distributions around Idealized Sources 221 Exercises 235 Chapter 9 Spherical Waves 237 9.1 Scalar Spherical Waves 237 9.2 Vector Spherical Waves 249 9.3 Isolated Multipole Fields 259 9.4 Multipole Sources 262 9.5 Spherical-Wave Constituents of Vector Plane Waves 272 Exercises 278 Chapter 10 Fields of a Moving Point Charge 283 10.1 The Lienard-Wiechert Potentials 283 10.2 Radiation by a Point Charge 288 10.3 Low-Velocity Radiation 290 10.4 Radiation at High Speeds 295 10.5 Continuous Spectra 298 10.6 The Field of a Uniformly Moving Point Charge 315 Exercises 321
CONTENTS Vll Chapter Chapter 11 11.1 11.2 11.3 11.4 12 12.1 12.2 12.3 Einstein's Special Theory of Relativity 324 Lorentz Transformations 326 The Relativistic Mass Particle 339 Energy-Momentum Conservation in Particle Reactions 348 Particle-Photon Interactions 363 Exercises 372 Frame-Independent Representations 376 Relativistically Covariant Field Descriptions 377 Electromagnetic Forces and Field Energy-Momentum 387 Relativistic Particle Dynamics 393 Exercises 401 Chapter 13 Field Dynamics and Conservation Laws 406 13.1 Alternative Formulations of Mechanics 407 13.2 The Field Lagrangian 416 13.3 Invariances and Conservation Laws 421 Chapter 14 Radiative Motions of a Point Charge 429 14.1 The Charge plus Self-Field System 429 14.2 Covariant Formulations of Point-Charge Radiations 436 14.3 The Nonrelativistic Lorentz-Abraham Equation 440 14.4 The Relativistic Lorentz-Dirac Equation 443 14.5 The Integrodifferential Equation of Motion 446 14.6 Linear Motions and Preacceleration 449 14.7 The Collapse of the Classical Atom 454 14.8 Classical Radiation Widths 461 Supplementary Chapters Mathematical Developments and Macroscopically Described Matter 467 Chapter A The Calculus of Fields 469 A.I Gradient, Divergence, and Curl Derivatives 469 A.2 Gradient Fields and Line Integrals 471 A.3 Divergences and Field Sources 472 A.4 Field Curl 475 A.5 The Laplacian 479 Exercises " 486
viii CONTENTS Chapter B The Electrostatics of Conductors 490 B.I Conducting Spaces 490 B.2 Conductor Boundaries 491 B.3 Image Charges in Conductors 493 B.4 The Conducting Sphere in a Uniform Field 497 B.5 Shielding by Conductors 498 B.6 Forces on Conductors. 500 Exercises 503 Chapter C Cylindrical Laplace Fields 507 C.I Polar Coordinate Representations 507 C.2 Cylindrical Harmonics 509 C.3 Fourier-Bessel Series 512 C.4 Modified Bessel Functions 515 Exercises 517 Chapter D The Electrostatics of Dielectrics 521 D.I Bound Charges. 522 D.2 The Electric Displacement Field 523 D.3 The Dielectric Constant 524 " D.4 The Potential Description 526 D.5 Dielectric Effects on Conductor Capacitance 527 D.6 Dielectric Boundary Conditions 528 D.7 Images in Dielectrics 530 : D.8 A Dielectric Sphere in a Uniform Field 532 D.9 The Interaction of a Point Charge with a Dielectric Sphere 534 D.10 Field Energies and Forces in Dielectrics 535 Exercises 537 Chapter E The Magnetostatics of Materials 541 E.I Magnetization 541 E.2 Magnetic Induction 542 E.3 Permeability. 544 E.4 Ferromagnetism and Permanent Magnets 546 E.5 Magnetic Shielding 548 E.6 The Field of a Permanent Magnet 552 Exercises 555 Chapter F Waves in Transparent Materials 557 F.I The General Maxwell Equations in Dielectrics 557 F.2 Plane Waves in Dielectrics 559 F.3 Reflection and Refraction Angles 560 F.4 The Fresnel Formulas 563 F.5 Polarization by Reflection 565 F.6 Reflected and Transmitted Intensities 566 F.7 Total Internal Reflection 568 F.8 Dispersion in Transparent Dielectrics 570 Exercises 577
CONTENTS IX Chapter G Conductors and Wave Fields 579 G.I ^Conductivity r 579 G.2 Wave Fields inside Conducting Media 581 G.3 Reflection and Transmission by Conductors 586 G.4 Current Distributions in Conductors 592 G.5 Conductivities at High Frequencies 599 Exercises 606 References Index 6io 6ii