Classical Electromagnetism in a Nutshell

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

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 xB 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