Classical Electromagnetism in a Nutshell

by Garg, Anupam

• ISBN13: 9780691130187
• ISBN10: 0691130183
• Format: Hardcover
• Copyright: 2012-03-19
• Publisher: Princeton Univ Pr

Summary

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 Nutshellis 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

Author Biography

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

Table of Contents

Preface	p. xv
List of symbols	p. xxi
Suggestions for using this book	p. xxxi
Introduction	p. 1
The field concept	p. 1
The equations of electrodynamics	p. 2
A lightspeed survey of electromagnetic phenomena	p. 7
SI versus Gaussian	p. 10
Review of mathematical concepts	p. 18
Vector algebra	p. 18
Derivatives of vector fields	p. 25
Integration of vector fields	p. 30
The theorems of Stokes and Gauss	p. 32
Fourier transforms, delta functions, and distributions	p. 37
Rotational transformations of vectors and tensors	p. 45
Orthogonal curvilinear coordinates	p. 51
Electrostatics in vacuum	p. 55
Coulomb's law	p. 55
The electrostatic potential	p. 57
Electrostatic energy	p. 58
Differential form of Coulomb's law	p. 63
Uniqueness theorem of electrostatics	p. 65
Solving Poisson's equation: a few examples	p. 68
Energy in the electric field	p. 71
The Multipole expansion	p. 73
Charge distributions in external fields	p. 80
Magnetostatics in vacuum	p. 82
Sources of magnetic field	p. 82
The law of Biot and Savart	p. 89
Differential equations of magnetostatics; Ampere's law	p. 93
The vector potential	p. 101
Gauge invariance	p. 105
∇ B and ∇ × B for a point dipole	p. 108
Magnetic multipoles	p. 112
Induced electromagnetic fields	p. 114
Induction	p. 114
Energy in the magnetic field-Feynman's argument	p. 117
Energy in the magnetic field-standard argument	p. 120
Inductance	p. 121
The Ampere-Maxwell law	p. 125
Potentials for time-dependent fields	p. 128
Symmetries and conservation laws	p. 132
Discrete symmetries of the laws of electromagnetism	p. 132
Energy flow and the Poynting vector	p. 137
Momentum conservation	p. 140
Angular momentum conservation*	p. 144
Relativity at low speeds	p. 148
Electromagnetic mass*	p. 150
Electromagnetic waves	p. 152
The wave equation for E and B	p. 152
Plane electromagnetic waves	p. 154
Monochromatic plane waves and polarization	p. 156
Nonplane monochromatic waves; geometrical optics*	p. 160
Electromagnetic fields in a laser beam*	p. 165
Partially polarized (quasimonochromatic) Hght*	p. 168
Oscillator representation of electromagnetic waves	p. 171
Angular momentum of the free electromagnetic field*	p. 174
Interference phenomena	p. 178
Interference and diffraction	p. 178
Fresnel diffraction	p. 182
Fraunhofer diffraction	p. 186
Partially coherent light	p. 187
The Hanbury-Brown and Twiss effect; intensity interferometry*	p. 191
The Pancharatnam phase*	p. 195
The electromagnetic field of moving charges	p. 200
Green's function for the wave equation	p. 200
Fields of a uniformly moving charge	p. 204
Potentials of an arbitrarily moving charge-the Lienard-Wiechert solutions	p. 207
Electromagnetic fields of an arbitrarily moving charge	p. 210
Radiation from accelerated charges: qualitative discussion	p. 214
Radiation from localized sources	p. 217
General frequency-domain formulas for fields	p. 217
Far-zone fields	p. 219
Power radiated	p. 223
The long-wavelength electric dipole approximation	p. 227
Higher multipoles*	p. 229
Antennas	p. 233
Near-zone fields	p. 237
Angular momentum radiated*	p. 239
Radiation reaction	p. 241
Motion of charges and moments in external fields	p. 245
The Lorentz force law	p. 245
Motion in a static uniform electric field	p. 246
Motion in a static uniform magnetic field	p. 248
Motion in crossed E and B fields; E < B	p. 251
Motion in a time-dependent magnetic field; the betatron	p. 255
Motion in a quasiuniform static magnetic field-guiding center drift*	p. 257
Motion in a slowly varying magnetic field-the first adiabatic invariant*	p. 261
The classical gyromagnetic ratio and Larmor's theorem	p. 264
Precession of moments in time-dependent magnetic fields*	p. 268
Action formulation of electromagnetism	p. 273
Charged particle in given field	p. 273
The free field	p. 276
The interacting system of fields and charges	p. 279
Gauge invariance and charge conservation	p. 283
Electromagnetic fields in material media	p. 285
Macroscopic fields	p. 286
The macroscopic charge density and the polarization	p. 289
The macroscopic current density and the magnetization	p. 293
Constitutive relations	p. 297
Energy conservation	p. 300
Electrostatics around conductors	p. 302
Electric fields inside conductors, and at conductor surfaces	p. 303
Theorems for electrostatic fields	p. 306
Electrostatic energy with conductors; capacitance	p. 308
The method of images	p. 313
Separation of variables and expansions in basis sets	p. 320
The variational method*	p. 329
The relaxation method	p. 334
Microscopic electrostatic field at metal surfaces; work function and contact potential*	p. 339
Electrostatics of dielectrics	p. 344
The dielectric constant	p. 344
Boundary value problems for linear isotropic dielectrics	p. 347
Depolarization	p. 350
Thermodynamic potentials for dielectrics	p. 354
Force on small dielectric bodies	p. 360
Models of the dielectric constant	p. 361
Magnetostatics in matter	p. 370
Magnetic permeability and susceptibility	p. 370
Thermodynamic relations for magnetic materials	p. 371
Diamagnetism	p. 375
Paramagnetism	p. 378
The exchange interaction; ferromagnetism	p. 378
Free energy of ferromagnets	p. 382
Ferromagnetic domain walls*	p. 391
Hysteresis in ferromagnets	p. 394
Demagnetization	p. 397
Superconductors*	p. 399
Ohm's law, emf, and electrical circuits	p. 404
Ohm's law	p. 405
Electric fields around current-carrying conductors-a solvable example*	p. 407
van der Pauw's method*	p. 409
The Van de Graaff generator	p. 412
The thermopile	p. 413
The battery	p. 414
Lumped circuits	p. 417
The telegrapher's equation*	p. 422
The ac generator	p. 424
Frequency-dependent response of materials	p. 427
The frequency-dependent conductivity	p. 427
The dielectric function and electric propensity	p. 429
General properties of the ac conductivity*	p. 431
Electromagnetic energy in material media*	p. 435
Drude-Lorentz model of the dielectric response	p. 437
Frequency dependence of the magnetic response*	p. 441
Quasistatic phenomena in conductors	p. 443
Quasistatic fields	p. 443
Variable magnetic field: eddy currents and the skin effect in a planar geometry	p. 445
Variable magnetic field: eddy currents and the skin effect in finite bodies*	p. 450
Variable electric field, electrostatic regime	p. 455
Variable electric field, skin-effect regime	p. 457
Eddy currents in thin sheets, Maxwell's receding image construction, and maglev*	p. 459
Motion of extended conductors in magnetic fields*	p. 465
The dynamo*	p. 467
Electromagnetic waves in insulators	p. 470
General properties of EM waves in media	p. 470
Wave propagation velocities	p. 472
Reflection and refraction at a fiat interface (general case)	p. 475
More reflection and refraction (both media transparent and nonmagnetic)	p. 479
Reflection from a nonmagnetic opaque medium*	p. 483
Electromagnetic waves in and near conductors	p. 487
Plasma oscillations	p. 487
Dispersion of plasma waves*	p. 488
Transverse EM waves in conductors	p. 490
Reflection of light from a metal	p. 492
Surface plasmons*	p. 493
Waveguides	p. 496
Resonant cavities	p. 502
Scattering of electromagnetic radiation	p. 505
Scattering terminology	p. 505
Scattering by free electrons	p. 506
Scattering by bound electrons	p. 508
Scattering by small particles	p. 510
Scattering by dilute gases, and why the sky is blue	p. 512
Raman scattering	p. 515
Scattering by liquids and dense gases*	p. 516
Formalism of special relativity	p. 524
Review of basic concepts	p. 524
Four-vectors	p. 532
Velocity, momentum, and acceleration four-vectors	p. 537
Four-tensors	p. 540
Vector fields and their derivatives in space-time	p. 543
Integration of vector fields*	p. 544
Accelerated observers*	p. 548
Special relativity and electromagnetism	p. 553
Four-current and charge conservation	p. 553
The four-potential	p. 556
The electromagnetic field tensor	p. 556
Covariant form of the laws of electromagnetism	p. 559
The stress-energy tensor	p. 561
Energy-momentum conservation in special relativity	p. 564
Angular momentum and spin*	p. 565
Observer-dependent properties of light	p. 567
Motion of charge in an electromagnetic plane wave*	p. 572
Thomas precession*	p. 576
Radiation from relativistic sources	p. 581
Total power radiated	p. 581
Angular distribution of power	p. 584
Synchrotron radiation-qualitative discussion	p. 588
Full spectral, angular, and polarization distribution of synchrotron radiation*	p. 589
Spectral distribution of synchrotron radiation*	p. 592
Angular distribution and polarization of synchrotron radiation*	p. 595
Undulators and wigglers*	p. 597
Spherical harmonics	p. 605
Bessel Junctions	p. 617
Time averages of bilinear quantities in electrodynamics	p. 625
Caustics	p. 627
Airy functions	p. 633
Power spectrum of a random function	p. 637
Motion in the earth's magnetic field-the Stormer problem	p. 643
Alternative proof of Maxwell's receding image construction	p. 651
Bibliography	p. 655
Index	p. 659
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