Classical electrodynamics

592 Pages·2019·38.537 MB·English

by  Deraad, Lester L., Milton, K. A., Schwinger, Julian, Tsai, Wu-yang

C l a s s i c a l
E le c t r D d y n a m ic s
Julian Schwinger • Lester L. DeRaad, Jr.
Kimball A. Milton • Wu-yang Tsai
A dvanced Book Program
CRC Press
Taylor & Francis Group
Boca Raton London New York
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The Advanced Book Program
First published 1998 by Westview Press
Published 2018 by CRC Press
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Copyright © 1998 by Clarice Schwinger, Lester DeRaad, Jr., Kimball A.
Milton, and Wu-yang Tsai
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Library of Congress Catalog Card Number: 98-86259
ISBN 13: 978-0-7382-0056-9 (hbk)
Cover design by Suzanne Heiser
To our children,
Elizabeth, Lester III
Ysabel, Madeleine, Camille
Tenno

Contents
Preface xvij
Reader’s Guide xix
1 Maxwell’s Equations 1
1.1 Electrostatics....................................................................................... 1
1.2 Inference of Maxwell’s Equations..................................................... 8
1.3 Discussion........................................... 12
1.4 Problems for Chapter 1 .................................................................... 13
2 Magnetic Charge I IT
2.1 A Very Brief History of Magnetic Charge..................................... 19
2.2 Problems for Chapter 2 .................................................................... 19
3 Conservation Laws 21
3.1 Conservation of Energy .................................................................... 21
3.2 Conservation of Momentum.............................................................. 22
3.3 Conservation of Angular Momentum. Virial Theorem ................ 24
3.4 Conservation Laws and the Speed of Light..................................... 25
3.5 Problems for Chapter 3 .................................................................... 29
4 Macroscopic Electrodynamics 33
4.1 Force on an Atom ............................................................................. 33
4.2 Force on a Macroscopic Body........................................................... 38
4.3 Macroscopic Electrodynamics..................... 40
4.4 Problems for Chapter 4 .................................................................... 42
5 Simple Model for Constitutive Relations 45
5.1 Conductivity....................................................................................... 45
5.2 Dielectric Constant............................................................................. 47
5.3 Plasma................................................................................................... 51
5.4 Polar Molecules................................................................................... 53
5.5 Clausius-Mossotti Equation.............................................................. 57
5.6 Problems for Chapter 5 .................................................................... 59
6 Magnetic Properties of Matter 63
6.1 Canonical Equations of Motion in Electromagnetic Fields . . . . 63
6.2 Diamagnetism....................................................................................... 65
v
vi CONTENTS
6.3 Paramagnetism.................................................................................... 67
6.4 Ferromagnetism.................................................................................... 69
6.5 Problems for Chapter 6 .................................................................... 72
7 Macroscopic Energy and Momentum 75
7.1 General Discussion.............................................................................. 75
7.2 Nondispersive Medium....................................................................... 77
7.3 Dispersive Medium.............................................................................. 77
7.4 Problems for Chapter 7 .................................................................... 80
8 Review of Action Principles 85
8.1 Lagrangian Viewpoint....................................................................... 86
8.2 Hamiltonian Viewpoint .................................................................... 87
8.3 A Third Viewpoint.............................................................................. 89
8.4 Invariance and Conservation Laws.................................................. 90
8.5 Nonconservation Laws. The Virial Theorem.................................. 94
8.6 Problems for Chapter 8 .................................................................... 95
9 Action Principle for Electrodynamics 97
9.1 Action of Particle in Field .................................................................. 97
9.2 Electrodynamic Action....................................................................... 98
9.3 Energy......................................................................................................100
9.4 Momentum and Angular Momentum Conservation.........................102
9.5 Gauge Invariance and the Conservation of Charge .........................105
9.6 Gauge Invariance and Local Conservation Laws...............................107
9.7 Problems for Chapter 9 .......................................................... 110
10 Einsteinian Relativity 111
10.1 Relativistic Modification.......................................................................Ill
10.2 Lorentz Transformations.......................................................................114
10.3 Transformation of Fields.......................................................................118
10.4 Problems for Chapter 10.......................................................................122
11 Stationary Principles for Electrostatics 125
11.1 Stationary Principles for the Energy..................................................126
11.1.1 The Scalar Field Form..............................................................127
11.1.2 The Vector Field Form..............................................................127
11.2 Force on Dielectrics............... 129
11.3 Boundary Conditions . ...........................................................................132
11.4 Conductors.............................................................................................134
11.5 Problems for Chapter 11.......................................................................135
12 Introduction to Green’s Functions 137
12.1 Reciprocity Relation................................................. . ...................138
12.2 Problems for Chapter 12.......................................................................139
CONTENTS vü
13 Electrostatics in Free Space 141
13.1 2+1 Dimensions................................................................................143
13.2 Problems for Chapter 13.......................................................................146
14 Semi-Infinite Dielectric 147
14.1 Green’s Function for Charge Outside Dielectric............................147
14.2 Derivation in Terms of Bound Charge...........................................150
14.3 Green’s Function for Charge Within Dielectric ............................153
14.4 Full Green’s Function and Image Charge........................................155
14.5 Problems for Chapter 14........................................................... . . . 156
15 Application of Green’s Function 157
15.1 Force between Charge and Dielectric.................................................157
15.2 Infinite Conducting Plate....................................................................161
15.3 Problems for Chapter 15.......................................................................163
16 Bessel Functions 165
16.1 Delta Functions and Completeness....................................................170
16.2 Problems for Chapter 16.......................................................................174
17 Parallel Conducting Plates 177
17.1 Reduced Green’s Function....................................................................177
17.2 Induced Charge......................................................................................179
17.3 Energy......................................................................................................180
17.4 Force............................................................................................... 182
17.5 Images........................... 183
17.6 Linear Lattices......................................................................................185
17.7 Periodic Green’s Function....................................................................186
17.8 Problems for Chapter 17......................................................... 189
18 Modified Bessel Functions 193
18.1 More Bessel Functions........................................... 197
18.2 Problems for Chapter 18.......................................................................203
19 Cylindrical Conductors 205
19.1 Rectangle................................................................................................205
19.2 Isosceles Right Angle Triangle..............................................................207
19.3 Equilateral Triangle .............................................................................208
19.4 Circle ......................................................................................................215
19.5 Circle and Septum................................................................................225
19.6 Problems for Chapter 19........................... 228
20 Spherical Harmonics 231
20.1 Solutions to Laplace’s Equation............... 231
20.2 Spherical Harmonics.............................................. . . . ................233
20.3 Orthonormality Condition..................... 236
20.4 Legendre’s Polynomials.......................................................................238
viii CONTENTS
20.5 Problems for Chapter 20 ................................................................... 238
21 Coulomb’s Potential 243
21.1 Legendre’s Polynomials.......................................................................244
21.2 Infinitesimal Rotations..........................................................................246
21.3 Spherical Bessel Functions....................................................................249
21.4 Problems for Chapter 21.......................................................................253
22 Multipoles 257
22.1 Problems for Chapter 22 .................................................................... 261
23 Conducting and Dielectric Spheres 265
23.1 Interior of Conducting SphericalS hell................................................265
23.1.1 Bessel Function Representation..............................................267
23.2 Exterior of Conducting Sphere .......................................................271
23.3 Conducting Plate and HemisphericalB oss..........................................274
23.4 Dielectric Sphere ................................................. 276
23.4.1 Interior of sphere.......................................................................278
23.5 Problems for Chapter 23 .................................................................... 280
24 Dielectrics and Conductors 283
24.1 Variational Principle................................................................ 283
24.2 Restricted Forms of the Variational Principle..................................285
24.3 Introduction of Additional Conductor ..............................................286
24.4 Alternate Variational Principle...........................................................288
24.5 Green’s Function...................................................................................289
24.6 Capacitance........................................................... . . ......................290
24.7 Problems for Chapter 24 .................................................................... 293
25 Modes and Variations 295
25.1 A Comparison Method............................................................. 301
25.2 Iteration...................................................................................................304
25.3 Example...................................................................................................311
25.4 Problems for Chapter 25 . . ..................................... 312
26 Magnetostatics 313
26.1 Variational Principle.............................................................................313
26.2 Boundary Conditions.............................................................................315
26.3 Vector Potential ...................................................................................316
26.4 Problems for Chapter 26.......................................................................318
27 Macroscopic Current Distributions 319
27.1 Magnetic Energy. Coefficients of Inductance............................ 322
27.2 Problems for Chapter 27 .................................................................. 323
CONTENTS IX
28 Magnetic Multipoles 325
28.1 Magnetic Dipole Moment....................................................................325
28.2 Rotating Charged Spherical Shell........................................................327
28.3 Problems for Chapter 28 .................................................................... 329
29 Magnetic Scalar Potential 331
29.1 Problems for Chapter 29 .................................................................... 334
30 Magnetic Charge II 337
30.1 Problems for Chapter 30 .................................................................... 339
31 Retarded Green’s Function 341
31.1 Potentials and Gauges..........................................................................341
31.2 Green’s Function in the Lorentz Gauge...........................................343
31.3 Problems for Chapter 31.......................................................................346
32 Radiation—Field Point of View 351
32.1 Asymptotic Potentials and Fields.......................................................351
32.2 Angular Distribution of Radiated Power............................................353
32.3 Radiation by an Accelerated Charged Particle..................................354
32.4 Dipole Radiation...................................................................................355
32.5 Potentials in Radiation Gauge.............................................................357
32.6 Problems for Chapter 32 .................................................................... 359
33 Radiation—Source Point of View 361
33.1 Conservation of Energy .......................................................................361
33.2 Dipole Radiation...................................................................................362
33.3 Hamiltonian............................................................................................363
33.4 Problems for Chapter 33 .................................................................... 366
34 Models of Antennas 367
34.1 Simplified M odel...................................................................................367
34.2 Center-fed antenna................................................................................371
34.3 Problems for Chapter 34..................................................................... 372
35 Spectral Distribution of Radiation 375
35.1 Spectral and Angular Distribution....................................................375
35.2 Spectral Distribution for Dipole Radiation........................................379
35.3 Damped Harmonic Motion....................................................................380
35.4 Problems for Chapter 35 .................................................................... 383
36 Power Spectrum and Cerenkov Radiation 385
36.1 Macroscopic Power Spectrum..............................................................385
36.2 Cerenkov Radiation .............................................................................386
36.3 Problems for Chapter 36 .................................................................... 389