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Classical Electromagnetism in a Nutshell
Anupam Garg

Book Description | Reviews
Preface [in PDF format] | Chapter 1 [in PDF format]

TABLE OF CONTENTS:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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File created: 7/11/2014

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