Ebook: Classical Electromagnetism in a Nutshell

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