### Classical Electromagnetism in a Nutshell (ISE)

**by Anupam Garg**

*Princeton University Press*

- Pub Date:
- 04/2012
- ISBN:
- 9780691130187
- Format:
- Hbk
*712 pages* - Price:
**AU$112.00***NZ$118.26*

**Product Status:**

*Not Our Publication - we no longer distribute***Instructors**

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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 along with a discussion of how to convert between them, making the book 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

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

“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

“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