ELECTROMAGNETIC FIELDS AND RELATIVISTIC PARTICLES

Transcription

1 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

2 CONTENTS Preface Introduction xi l Chapter 1 The Maxwell Equations Electric Charge 1.2 Magnetism 1.3 Induction Processes Exercises Chapter 2 The Electrostatic Field Superpositions of Coulomb Forces The Electrostatic Potential Static Multipoles Electrostatic Forces and Energies 39 Exercises 50 Chapter 3 Laplace Fields General Forms for the Potential,. 3.2 Fourier Analysis 3.3 Spherical Representations Exercises Chapter 4 The Magnetostatic Field The Generation of Magnetostatic Fields by Currents The Magnetic Dipole Approximation Magnetic Forces Magnetostatic Energy 110 Exercises

3 VI CONTENTS Chapter 5 Nonrelativistic Motions in Static Fields A Point Charge in a Uniform Magnetic Field The E x B Drift Magnetic Dipoles in Magnetic Fields The Magnetic Mirror Effect The Rotation of Dipoles 139 Exercises 147 Chapter 6 Describing the General Electromagnetic Field Field Energy and Its Flux Field Momentum and Stress Field Angular Momentum Nonstatic Potentials 170 Exercises 178 Chapter 7 Plane Electromagnetic Waves Wave Fields in Free Space Plane Monochromatic Waves 186 ' 7.3 Wave Fields within Perfectly Reflecting Boundaries 192 Exercises 204 Chapter 8 The Generation of Electromagnetic Waves Retarded Potentials Radiation from Monochromatic Sources Field Distributions around Idealized Sources 221 Exercises 235 Chapter 9 Spherical Waves Scalar Spherical Waves Vector Spherical Waves Isolated Multipole Fields Multipole Sources Spherical-Wave Constituents of Vector Plane Waves 272 Exercises 278 Chapter 10 Fields of a Moving Point Charge The Lienard-Wiechert Potentials Radiation by a Point Charge Low-Velocity Radiation Radiation at High Speeds Continuous Spectra The Field of a Uniformly Moving Point Charge 315 Exercises 321

4 CONTENTS Vll Chapter Chapter 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 Alternative Formulations of Mechanics The Field Lagrangian Invariances and Conservation Laws 421 Chapter 14 Radiative Motions of a Point Charge The Charge plus Self-Field System Covariant Formulations of Point-Charge Radiations The Nonrelativistic Lorentz-Abraham Equation The Relativistic Lorentz-Dirac Equation The Integrodifferential Equation of Motion Linear Motions and Preacceleration The Collapse of the Classical Atom 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

5 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

6 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