Classical Electromagnetism in a Nutshell

by Anupam Garg

Overview

A comprehensive, modern introduction to electromagnetism

This graduate-level physics textbook provides a comprehensive treatment of the basic principles and phenomena of classical electromagnetism. While many electromagnetism texts use the subject to teach mathematical methods of physics, here the emphasis is on the physical ideas themselves. Anupam Garg distinguishes between electromagnetism in vacuum and that in material media, stressing that the core physical questions are different for each. In vacuum, the focus is on the fundamental content of electromagnetic laws, symmetries, conservation laws, and the implications for phenomena such as radiation and light. In material media, the focus is on understanding the response of the media to imposed fields, the attendant constitutive relations, and the phenomena encountered in different types of media such as dielectrics, ferromagnets, and conductors. The text includes applications to many topical subjects, such as magnetic levitation, plasmas, laser beams, and synchrotrons.

Classical Electromagnetism in a Nutshell is ideal for a yearlong graduate course and features more than 300 problems, with solutions to many of the advanced ones. Key formulas are given in both SI and Gaussian units; the book includes a discussion of how to convert between them, making it accessible to adherents of both systems.

• Offers a complete treatment of classical electromagnetism
• Emphasizes physical ideas
• Separates the treatment of electromagnetism in vacuum and material media
• Presents key formulas in both SI and Gaussian units
• Covers applications to other areas of physics
• Includes more than 300 problems

Product Details

ISBN-13:	9780691130187
Publisher:	Princeton University Press
Publication date:	04/08/2012
Series:	In a Nutshell , #13
Edition description:	New Edition
Pages:	712
Product dimensions:	7.10(w) x 10.10(h) x 1.70(d)

About the Author

Anupam Garg is professor of physics and astronomy at Northwestern University.

Table of Contents

Preface xv
List of symbols xxi
Suggestions for using this book xxxi

Chapter 1 Introduction 1
1The field concept 1
2The equations of electrodynamics 2
3A lightspeed survey of electromagnetic phenomena 7
4SI versus Gaussian 10

Chapter 2 Review of mathematical concepts 18
5Vector algebra 18
6Derivatives of vector fields 25
7Integration of vector fields 30
8The theorems of Stokes and Gauss 32
9Fourier transforms, delta functions, and distributions 37
10Rotational transformations of vectors and tensors 45
11Orthogonal curvilinear coordinates 51

Chapter 3 Electrostatics in vacuum 55
12Coulomb’s law 55
13The electrostatic potential 57
14Electrostatic energy 58
15Differential form of Coulomb’s law 63
16Uniqueness theorem of electrostatics 65
17Solving Poisson’s equation: a few examples 68
18Energy in the electric field 71
19The multipole expansion 73
20Charge distributions in external fields 80

Chapter 4 Magnetostatics in vacuum 82
21Sources of magnetic field 82
22The law of Biot and Savart 89
23Differential equations of magnetostatics; Ampere’s law 93
24The vector potential 101
25Gauge invariance 105
26∇ B and ∇×B for a point dipole 108
27Magnetic multipoles 112

Chapter 5 Induced electromagnetic fields 114
28Induction 114
29Energy in the magnetic field—Feynman’s argument 117
30Energy in the magnetic field—standard argument 120
31Inductance 121
32The Ampere-Maxwell law 125
33Potentials for time-dependent fields 128

Chapter 6 Symmetries and conservation laws 132
34Discrete symmetries of the laws of electromagnetism 132
35Energy flow and the Poynting vector 137
36Momentum conservation 140
37Angular momentum conservation∗ 144
38Relativity at low speeds 148
39Electromagnetic mass∗ 150

Chapter 7 Electromagnetic waves 152
40The wave equation for E and B 152
41Plane electromagnetic waves 154
42Monochromatic plane waves and polarization 156
43Nonplane monochromatic waves; geometrical optics∗ 160
44Electromagnetic fields in a laser beam∗ 165
45Partially polarized (quasimonochromatic) light∗ 168
46Oscillator representation of electromagnetic waves 171
47Angular momentum of the free electromagnetic field∗ 174

Chapter 8 Interference phenomena 178
48Interference and diffraction 178
49Fresnel diffraction 182
50Fraunhofer diffraction 186
51Partially coherent light 187
52The Hanbury-Brown and Twiss effect; intensity interferometry∗ 191
53The Pancharatnam phase∗ 195

Chapter 9 The electromagnetic field of moving charges 200
54Green’s function for the wave equation 200
55Fields of a uniformly moving charge 204
56Potentials of an arbitrarily moving charge—the Lienard-Wiechert solutions 207
57Electromagnetic fields of an arbitrarily moving charge 210
58Radiation from accelerated charges: qualitative discussion 214

Chapter 10 Radiation from localized sources 217
59General frequency-domain formulas for fields 217
60Far-zone fields 219
61Power radiated 223
62The long-wavelength electric dipole approximation 227
63Higher multipoles∗ 229
64Antennas 233
65Near-zone fields 237
66Angular momentum radiated∗ 239
67Radiation reaction 241

Chapter 11 Motion of charges and moments in external fields 245
68The Lorentz force law 245
69Motion in a static uniform electric field 246
70Motion in a static uniform magnetic field 248
71Motion in crossed E and B fields; E < B 251
72Motion in a time-dependent magnetic field; the betatron 255
73Motion in a quasiuniform static magnetic field—guiding center drift∗ 257
74Motion in a slowly varying magnetic field—the first adiabatic invariant∗ 261
75The classical gyromagnetic ratio and Larmor’s theorem 264
76Precession of moments in time-dependent magnetic fields∗ 268

Chapter 12 Action formulation of electromagnetism 273
77Charged particle in given field 273
78The free field 276
79The interacting system of fields and charges 279
80Gauge invariance and charge conservation 283

Chapter 13 Electromagnetic fields in material media 285
81Macroscopic fields 286
82The macroscopic charge density and the polarization 289
83The macroscopic current density and the magnetization 293
84Constitutive relations 297
85Energy conservation 300

Chapter 14 Electrostatics around conductors 302
86Electric fields inside conductors, and at conductor surfaces 303
87Theorems for electrostatic fields 306
88Electrostatic energy with conductors; capacitance 308
89The method of images 313
90Separation of variables and expansions in basis sets 320
91The variational method∗ 329
92The relaxation method 334
93Microscopic electrostatic field at metal surfaces; work function and contact potential∗ 339
15Electrostatics of dielectrics 344
94The dielectric constant 344
95Boundary value problems for linear isotropic dielectrics 347
96Depolarization 350
97Thermodynamic potentials for dielectrics 354
98Force on small dielectric bodies 360
99Models of the dielectric constant 361

Chapter 16 Magnetostatics in matter 370
100 Magnetic permeability and susceptibility 370
101Thermodynamic relations for magnetic materials 371
102Diamagnetism 375
103Paramagnetism 378
104The exchange interaction; ferromagnetism 378
105Free energy of ferromagnets 382
106Ferromagnetic domain walls∗ 391
107Hysteresis in ferromagnets 394
108Demagnetization 397
109Superconductors∗ 399

Chapter 17 Ohm’s law, emf, and electrical circuits 404
110Ohm’s law 405
111Electric fields around current-carrying conductors—a solvable example∗ 407
112van der Pauw’s method∗ 409
113The Van de Graaff generator 412
114The thermopile 413
115The battery 414
116Lumped circuits 417
117The telegrapher’s equation∗ 422
118The ac generator 424

Chapter 18 Frequency-dependent response of materials 427
119The frequency-dependent conductivity 427
120The dielectric function and electric propensity 429
121General properties of the ac conductivity∗ 431
122Electromagnetic energy in material media∗ 435
123Drude-Lorentz model of the dielectric response 437
124Frequency dependence of the magnetic response∗ 441
19Quasistatic phenomena in conductors 443
125Quasistatic fields 443
126Variable magnetic field: eddy currents and the skin effect in a planar geometry 445
127Variable magnetic field: eddy currents and the skin effect in finite bodies∗ 450
128Variable electric field, electrostatic regime 455
129Variable electric field, skin-effect regime 457
130Eddy currents in thin sheets, Maxwell’s receding image construction, and maglev∗ 459
131Motion of extended conductors in magnetic fields∗ 465
132The dynamo∗ 467

Chapter 20 Electromagnetic waves in insulators 470
133General properties of EM waves in media 470
134Wave propagation velocities 472
135Reflection and refraction at a flat interface (general case) 475
136More reflection and refraction (both media transparent and nonmagnetic) 479
137Reflection from a nonmagnetic opaque medium∗ 483

Chapter 21 Electromagnetic waves in and near conductors 487
138Plasma oscillations 487
139Dispersion of plasma waves∗ 488
140Transverse EM waves in conductors 490
141Reflection of light from a metal 492
142Surface plasmons∗ 493
143Waveguides 496
144Resonant cavities 502

Chapter 22 Scattering of electromagnetic radiation 505
145Scattering terminology 505
146Scattering by free electrons 506
147Scattering by bound electrons 508
148Scattering by small particles 510
149Scattering by dilute gases, and why the sky is blue 512
150Raman scattering 515
151Scattering by liquids and dense gases∗ 516

Chapter 23 Formalism of special relativity 524
152Review of basic concepts 524
153Four-vectors 532
154Velocity, momentum, and acceleration four-vectors 537
155Four-tensors 540
156Vector fields and their derivatives in space—time 543
157Integration of vector fields∗ 544
158Accelerated observers∗ 548

Chapter 24 Special relativity and electromagnetism 553
159Four-current and charge conservation 553
160The four-potential 556
161The electromagnetic field tensor 556
162Covariant form of the laws of electromagnetism 559
163The stress—energy tensor 561
164Energy—momentum conservation in special relativity 564
165Angular momentum and spin∗ 565
166Observer-dependent properties of light 567
167Motion of charge in an electromagnetic plane wave∗ 572
168Thomas precession∗ 576

Chapter 25 Radiation from relativistic sources 581
169Total power radiated 581
170Angular distribution of power 584
171Synchrotron radiation—qualitative discussion 588
172Full spectral, angular, and polarization distribution of synchrotron radiation∗ 589
173Spectral distribution of synchrotron radiation∗ 592
174Angular distribution and polarization of synchrotron radiation∗ 595
175Undulators and wigglers∗ 597

Appendix A: Spherical harmonics 605
Appendix B: Bessel functions 617
Appendix C: Time averages of bilinear quantities in electrodynamics 625
Appendix D: Caustics 627
Appendix E: Airy functions 633
Appendix F: Power spectrum of a random function 637
Appendix G: Motion in the earth’s magnetic field—the Stormer problem 643
Appendix H: Alternative proof of Maxwell’s receding image construction 651
Bibliography 655
Index 659

What People are Saying About This

From the Publisher

"This text provides a fresh, modern look at electrodynamics. It is comprehensive, chock full of interesting insights and anecdotes, and written with a clear enthusiasm."—Kenneth A. Intriligator, University of California, San Diego

"Garg displays considerable wisdom and courage in writing a long-overdue, modern treatment of electromagnetism. I wish I had this book when I was a student. It contains delightful morsels of deep insight (the introduction taught me that fields are as real as a rhinoceros, or as I might extend it, 'quantum fields are as real as quantum rhinos') and interesting topics that are rarely, if ever, treated in other texts."—A. Zee, author of Quantum Field Theory in a Nutshell

"Garg demonstrates that while the mathematical beauty of his subject is deserving of the attention it gets, the physical implications are even more seductive. This book is a treasure trove of thoughtful and incisive nuggets. I expect to see it on the shelves of many students and professors the world over."—R. Shankar, Yale University

"An outstanding text. It offers delightful insights into the physics of electromagnetism rather than treating this subject as an excuse for laborious exercises in mathematical methods. It has the best treatment of electromagnetism in material media that I know. Remarkably lucid and enjoyable, and a worthy competitor to Jackson's classic text."—Jainendra Jain, Pennsylvania State University

"Classical Electromagnetism in a Nutshell is an interesting and elegant book, and an excellent text for a graduate-level course on the subject. Garg has a lively, modern writing style that will engage today's graduate students."—John D. Stack, University of Illinois, Urbana-Champaign

"Garg's textbook is truly excellent. It goes the extra mile to provide physical insight in ways that will enhance students' understanding, and includes rarely seen topics as well. I want to compliment the author on the obvious care and expertise with which he assembled this text. If I were to teach a yearlong graduate-level electromagnetism course, I would use this book."—John W. Belcher, Massachusetts Institute of Technology

Editorial Reviews

"This is a very comprehensive book on classical electromagnetism covering historical introductions, detailed theoretical derivations with additional mathematical clarifications whenever necessary, practical applications, and numerous exercises and examples for teachers and students in this subject. It can certainly be a useful text-book for students as well as a good reference book for professionals in various fields of electromagnetism."—-Vladimir Cadez, Zentralblatt MATH

From the Publisher