Cambridge University Press 978-1-108-42041-9 — Introduction to Electrodynamics 4Th Edition David J

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Cambridge University Press 978-1-108-42041-9 — Introduction to Electrodynamics 4th Edition David J. Griffiths Index More Information

Index

Abraham-Lorentz formula, 489, Azimuthal angle, 38, 43 Brewster’s angle, 410 492–496, 573 Azimuthal symmetry, 141 Buckminsterfullerine, 161 Absorption, 412–417 Absorption coefficient, 422 BAC-CAB rule, 8 Canonical momentum, 443 Acausality, 441, 446–447, 490 Back emf, 325, 328 Capacitance, 105 Acceleration Ball, defined, 51 Capacitor, 104–107 ordinary, 549 Bar electret, 176, 184 charging, 106–107, 336–337 proper, 549 Bar magnet, 276, 284 dielectric-filled, 190 Acceleration field, 460, 482 Barn and ladder paradox, 516–518 discharging, 302 Advanced potentials, 446 Betatron, 348 energy in, 106–107, 197 Advanced time, 446 Biot-Savart law, 224–228, 351, parallel-plate, 75, 105, 190, Alfven’s theorem, 352 560 240, 553 Ampere (unit), 216, 224 Bohr atom Cartesian coordinates, 4, Ampère, A. M., xvi lifetime, 487 130–131, 575 Ampère dipole, 269, 294 polarizability, 169–170 Cauchy’s formula, 424 Ampère’s law, 233, 243, Bohr magneton, 263 Causality, 441, 446–447, 489, 332–337, 567 Bound charge, 173–179, 192, 340 531 applications of, 233–241 Bound currents, 274–277, 287, 340 Cavity in matter, 279–282 physical interpretation of, in conductor, 99–100, 120 symmetry for, 237 277–279 in dielectric, 183–184 Amperian loop, 233, 249 Boundary conditions in magnetic material, 282–283 Amplitude of wave, 385 for dielectrics, 185, 188, resonant, 435 Angle 192–197, 206, 342–344 Center of energy, 546–547 azimuthal, 38, 43 for electrodynamics, 53, Center of momentum, 537 of incidence, 407 342–344 Cgs units, xviii, 585–588 polar, 38 for electromagnetic waves, Charge of reflection, 407 402, 406, 416 bound, 173–179, 192, 340 of refraction, 407 for electrostatics, 88–91 conservation of, xvii, 222, 339 Angular frequency, 386 for Laplace’s equation, (see also Continuity Angular momentum, 370–373, 119–124 equation) 378–380 for magnetic materials, 284, local, 566 Angular momentum density, 372 293, 342–344 electric, xvii–xviii, 59 Anomalous dispersion, 422–423 for magnetostatics, 249–251 enclosed, 69 Antisymmetric tensor, 562–564 for Maxwell’s equations, 338, free, 167, 181, 192, 412–413 Atomic polarizability, 168, 342–347, 583 induced, 98–102 208–209 for waves on a string, 388–391 magnetic (see Monopole) Auxiliary fields Boundary value problems, quantization, xvii–xviii, 380 D, 181–189, 281–283, 573 124–150, 192–197 uniformly moving, 461–463, H, 279–285, 573 Bremsstrahlung, 487 560

589

590 Index

Charge density spherical, 38–43, 575, 576 Delta function line, 63 translation of, 12 Dirac, 45–52, 164 surface, 63, 102 Cosines, law of, 3 Kronecker, 165, 363 volume, 63 Coulomb (unit), 60, 585 Density of field lines, 67 Charge invariance, 553 Coulomb field, generalized, 460 Derivative, 13 Child-Langmuir law, 109 Coulomb gauge, 440–441, 569 normal, 90 Circular polarization, 393 Coulomb’s law, xviii, 60, 63–64 Diamagnetism, 266, 271–274, Clausius-Mossotti equation, magnetic, 339 346, 349 208–209 Covariant vector, 526–527, 570 Dielectric, 167 Coaxial cable, 76, 431–432 Critical angle, 433 linear, 185–193 Colliding beam, 541–542 Cross product, 3, 6 Dielectric constant, 186, 187 Collision Curie point, 291 Diode, vacuum, 109 classical, 508 Curl, 16, 18–19, 579–581 Dipole moment, 155 elastic, 540 of A, 243, 436 Dipoles, electric, 67, 151, 154–160 relativistic, 540–543 of B, 229–233 energy of, in electric field, 172 Completeness, 135 in curvilinear coordinates, energy of interaction of two, Complex amplitude, 387 580–581 172 Complex notation, 387, 400 in cylindrical coordinates, 44 field of wave number, 422 of D, 184–185 oscillating, 470 Complex permittivity, 421 of E, 66, 77–78, 313 static, 67, 158–160 Complex susceptibility, 421 of H, 280 force on, 170–172 Component, 5, 39 in spherical coordinates, 42 induced, 167–170 Compton scattering, 540–541 Curl-less fields, 53, 78–80 perfect, 155, 159 Compton wavelength, 541 Current, 216–223 permanent, 170 Conductivity, 296–297 bound, 274–279, 287 physical, 155, 159 Conductors, 97–112, 167, 296 displacement, 334–335 potential of “good” and “poor,” 412 enclosed, 230, 233, 280, oscillating, 469 perfect, 296, 346, 352, 425 333–334 static, 151–152, 154–155 surface charge on, 125–126, free, 280, 287 radiation, 467–473 129, 299 induced, 315 torque on, 170–171 Conservation laws, 356–381. See polarization, 340–341 Dipoles, magnetic, 252–255 also Charge; Energy steady, 223 Ampère model, 269, 294 global, xvii, 356 Current density, 220–223 of electron, 263 local (see Continuity equation) four-vector, 565–566 energy of, in magnetic field, relativistic, 536–542 surface, 220 291 Conservative force, 25 volume, 220–221 energy of interaction of two, Constitutive relation, 186, 285, Curvilinear coordinates, 38, 292 342, 573 575–581 field of Continuity equation, xvii, 222, Cutoff frequency, 429–431 oscillating, 475–476 224, 338, 356–357, 359, Cycloid motion, 213–215, static, 255, 263–265 367, 565 545–546 force on, 267–270, 292–293 Contravariant vector, 526, 570 Cyclotron motion, 212–213, Gilbert model, 269, 294, 477 Convective derivative, 443 544–545 moment, 253–254, 265 Coordinates Cylindrical coordinates, 43–45, moving, 571–572 Cartesian, 4, 575, 576 575, 576 perfect, 254–255 curvilinear, 38, 575–581 physical, 254–255 cylindrical, 43–45, 575, 576 D. See Displacement, electric potential of inversion of, 12 D’Alembertian, 441–442, 570 oscillating, 475–476 rotation of, 10–12 Del operator, 16 static, 255

Index 591

radiation, 473–477, 482 Einstein, A., 314, 503–504 continuous charge Thomson’s dipole, 380 Einstein summation convention, distribution, 63 torque on, 266–270 527 dielectric cylinder in Dirac, P. A. M., 380 Einstein velocity addition rule, external field, 196 Dirac delta function, 45–52, 164 507–508, 523–524 dielectric sphere in external Dirichlet’s theorem, 134 Einstein’s postulates, 501–507 field, 192–194 Discharge of capacitor, 302 Elastic collision, 540 dipole, 158–160, 163 Discontinuity Electret, 176, 184 disk, 65 in B, 250, 284 Electric field, 59, 61–62. See finite line, 64–65 in E, 88–90 also Charge; Current; infinite cylinder, 73–74 Dispersion, 417–424 Dipoles, electric; infinite line, 65, 76 anomalous, 422–423 Displacement, electric; infinite plane, 74 Dispersion coefficient, 424 Energy; Force: electric; line charge, 63 Displacement, electric, 181–185 Polarization (of a overlapping spheres, 76, Displacement current, 334–337, medium); Potential; 178–179 342, 352 Susceptibility parallel-plate capacitor, 75 Displacement vector average over a sphere, 163 point charge distribution, 61 finite, 1, 8–9 in conductor, 98, 296–297 point charge near four-vector, 528 curl of, 66 conducting plane, infinitesimal divergence of, 66 124–125 Cartesian, 9 of dynamic configurations point charge near dielectric curvilinear, 575 arbitrary charge plane, 194–197 cylindrical, 44 distribution, 448, polarized object, 173–176 spherical, 40 479–480 ring, 65 Divergence, 16, 17, 577–579 oscillating electric dipole, sphere, 65, 71–72 of A, 243 470 spherical shell, 65, 76 of B, 229–232 oscillating magnetic dipole, surface charge distribution, in Cartesian coordinates, 17 476 63 in curvilinear coordinates, 578 parallel-plate capacitor, in cylindrical coordinates, 44 moving, 553–555, uniformly polarized of E, 66, 71 560–561 cylinder, 179 four-dimensional, 566 point charge, arbitrary uniformly polarized object, of H, 282–283 motion, 456–460 173–174, 293 in spherical coordinates, 42 point charge, constant uniformly polarized sphere, Divergence theorem, 32, 579 velocity, 460–461, 174–176 Divergenceless fields, 54, 249 555–556 volume charge distribution, Domain, 288–290 point charge moving in 63 Dot product, 2, 5, 526 straight line, 462 Electromagnetic force between Drift velocity, 300 rotating electric dipole, 473 point charges, 460–461 Drude, P. K. I., 300 induced, 313–314, 316–321 Electromagnetic induction, Dual tensor, 564, 573 macroscopic, 179–181, 199 312–332 Duality transformation, microscopic, 179–181 Electromagnetic mass, 495 353–354, 477 of static configurations Electromagnetic paradox, 495 Dumbbell model, 492–493 bar electret, 176, 184 Electromagnetic radiation, conducting sphere in xvi–xvii, 466 Earnshaw’s theorem, 118, 206 dielectric medium, Electromagnetic spectrum, 396 Earth’s magnetic field, 224 207–208 Electromagnetic waves. See Eddy currents, 310 conducting sphere in Waves Ehrenfest’s paradox, 518 external field, 146–147 Electromotance, 304

592 Index

Electromotive force (emf), Energy-momentum four-vector, on point charge near 296–312, 325 536 dielectric plane, 194–197 Electrons Equipotential, 80, 98 between point charges, 60, dipole moment, 263 Equivalence principle, 501 460–461 discovery of, 216 Ether, 504–506 on surface charge, 103–104 spin, 263–264, 379 drag, 505 electromagnetic, between Electrostatic pressure, 104 wind, 504–506 point charges, 460–461 Electrostatics, 59, 199, 223, 234, Euler’s formula, 387 Lorentz, 212, 217, 545 241–242 Evanescent wave, 434 magnetic Emf (electromotive force), Events, 519 on current, 217–218, 220–221 296–312, 325 Ewald-Oseen extinction between current loops, 259 Enclosed charge, 69 theorem, 401 on magnetic dipole, Enclosed current, 230, 233, 280, 267–270, 292 333–334 Farad (unit), 105 on magnetized material, 273 Energy Faraday, M., xvi, 312 between monopoles, 339 of capacitor, 107 Faraday cage, 102 between parallel currents, of charge in static field, 91–92 Faraday’s law, 312–321, 332, 210–212, 226, 229, conservation of, 405, 536 (see 395–397, 568 549–551 also Poynting’s theorem) Ferromagnetic domain, 288–290 between parallel planes, 240 of continuous charge Ferromagnetism, 266, 288–292 on point charge, 212 Feynman disk paradox, 371–373 distribution, 94–96 Minkowski, 545, 549, 568, Field, 54. See also Electric field; 571 of dipole, 172, 291–292 Magnetic field ordinary, 542, 545 in electric field, 357–359 Field line, 67–68 relativistic, 542 of electromagnetic wave, Field point, 9, 61 Force density, 362 398–400 Field tensor, 562–565, 569 Four vector, 525–528 of inductor, 328 Field theory, xvi, 52–55, acceleration, 549 of linear dielectric, 197–202 553–554 charge/current, 565–566 in magnetic field, 328–332, Flux displacement, 528 357 electric, 68–70 energy/momentum, 536 of point charge distribution, magnetic, 306, 311 gradient, 570 92–94 Flux density, 282 Minkowski force, 545, 549, of point charge near energy, 358 568, 571 conducting plane, 127 Flux integral, 24 position/time, 525–526 of spherical shell, 95–96 Flux rule, 307–310, 313–314, potential, 569–571 of static charge distribution, 503–504 velocity, 533–534 91 Flux rule paradox, 309 Fourier series, 134 Energy, relativistic, 536 Force Fourier transform, 388, 432 kinetic, 536 conservative, 25 Fourier’s trick, 134, 144 rest, 536 electric Frequency, 386 Energy density on conductor, 103–104 cutoff, 429–431 electromagnetic, 359, on dielectric, 202–204, Fresnel equations, 409–411 398–399 207–208 Fringing field, 202–203 of electromagnetic wave, on electric dipole, 170–172 Fundamental theorem of 398–400 on point charge in field, 61, calculus, 29 electrostatic, 94–97 212 for curls, 34 in linear media, 198 on point charge near for divergences, 31–32, 579 magnetostatic, 329–330 conducting plane, for gradients, 29–30, 577 Energy flux, 358 126–127 Future, 529–530

Index 593

Galilean transformation, Hertz, H., xvi, 335 time-reversal, 447 519–520, 527 Hidden momentum, 547–549 Invariant, 526, 536–537, 562, Galileo Galilei, 502 Homogeneous medium, 189 565 principle of relativity, 502 Horizon, 456 Invariant interval, 526–529 velocity addition rule, 507, 508 Hyperbolic geometry, 530–532 Invariant product, 526 Gauge Hyperbolic motion, 456, 463–464, Inversion, 12, 432 Coulomb, 440–441, 569 501, 535, 543, 571 Irrotational field, 53, 78–80 Lorentz, 441–442, 464, 570 Hysteresis, 290 Isotropic medium, 190 Gauge invariance, 570 Gauge transformation, 439–440 Images, method of, 124–130 Jefimenko’s equations, 449–451 Gauss (unit), 224, 588 dipole and conducting plane, Joule heating law, 301 Gaussian “pillbox,” 74–75 172 Jumping ring, 316 Gaussian surface, 71–74 parallel cylinders, 131 Gaussian units, xviii, 586–588 point charge and conducting Kinetic energy, 536 Gauss’s law, 68–70, 241, 332, plane, 124–127, 500 Kronecker delta, 165, 363 567 point charge and conducting applications of, 71–76 sphere, 127–130 Langevin equation, 209 inside matter, 181–183 point charge and dielectric Laplace’s equation, 84, 113–119 symmetry for, 72–73 plane, 196 in one dimension, 114–115 Gauss’s theorem, 32 Incidence in three dimensions, 117–119 Gedanken (thought) experiment, angle of, 407 in two dimensions, 115–117 508 plane of, 406–407 Laplacian, 23 Generator, 305–312 Incident wave, 388, 403 in Cartesian coordinates, 22, Gilbert dipole, 269, 294, 477 Induced charge, 98–102, 114 Gradient, 13, 14, 576 125–126, 130 in curvilinear coordinates, 581 in Cartesian coordinates, 13, 14 Induced current, 315 in cylindrical coordinates, 44 in curvilinear coordinates, 576 Induced dipole, 167–170 of a scalar, 23 in cylindrical coordinates, 44 Induced electric field, 313–314, in spherical coordinates, 42 four-dimensional, 570 316–321 of V, 84, 88, 113 in spherical coordinates, 42 Induced emf, 313–314 of a vector, 23–24 theorem, 29, 577 Inductance, 321–327 Larmor formula, 481, 484 Green’s identity, 57, 124 mutual, 321–323, 332 LC circuit, 327 Green’s reciprocity theorem, 164 self, 324–327, 331 Left-handed coordinates, 6 Green’s theorem, 32, 57 Induction, 282, 312–332 Legendre polynomials, 142, 153 Ground, 121 Inertial system, 502 Lenz’s law, 315–316 Group velocity, 418, 429 Inhomogeneous wave equation, Levi-Civita symbol, 292 Guided wave, 425–432 442 Levitation, 347 Gyromagnetic ratio, 263 Insulator, 97, 167 Liénard formula, 485, 573 Integration by parts, 36–37 Liénard-Wiechert potentials, H, 279–285 Intensity, 399 451–456, 463–464 Hall effect, 257 Internal reflection, 433 Lifetime, 511, 513 Harmonic function, 114 Internal resistance, 304, 305 Light, 382–435 Heaviside fields, 461–– 462, 555 556 Interval, spacetime, 528–529 speed of Heaviside-Lorentz units, xviii, 587 lightlike, 528, 530–531 linear medium, 401–402 Heaviside t heta function, 50 spacelike, 528, 530–531 universal, 506–507 Helical motion, 213 timelike, 528, 530–531 in vacuum, 394, 505–506 Helmholtz coil, 259 Invariance Light cone, 530 Helmholtz theorem, 52–53, 582–584 of charge, 553 Lightlike interval, 528 Henry (unit), 324 of mass, 537 Line charge, 63

594 Index

Line current, 216–217 charging capacitor, 336–337 Magnetization, 266–274, Line element oscillating electric dipole, 340–342 Cartesian, 9 470 Magnetomechanical ratio, 263 curvilinear, 575 oscillating magnetic dipole, Magnetostatics, 223, 234, 241, cylindrical, 44 475–476 249, 351–352 spherical, 40 parallel-plate capacitor, Mass Line integral, 24 moving, 556–558 electromagnetic, 495 Linear algebra, 11 point charge, arbitrary relativistic, 536 Linear combination, 133, 387–388 motion, 228, 456–461 rest, 536 Linear equation, 133, 385 point charge, constant Mass renormalization, 495 Linear medium, 401–402 velocity, 462, 560 Massless particle, 538–541 electric, 185–193 solenoid, moving, 558–559 Matrix magnetic, 284–287 of earth, 224, 498 Lorentz transformation, Linear polarization, 393 macroscopic, 279 525–526 Local conservation. See microscopic, 279 rotation, 11 Continuity equation of static configurations Maxwell, J. C., xvi, 332–335, Longitudinal wave, 391–392 bar magnet, 276, 284 394 Lorentz, H. A., xvi, 492, 506 in cavity, 282–283 Maxwell stress tensor, 362–366 Lorentz contraction, 506, circular loop, 227 Maxwell’s equations, 241, 514–518, 522 dipole, 255, 263–265 332–339, 567, 570 Lorentz contraction paradox, finite solenoid, 229 in Gaussian units, 588 515–516 finite straight line, 225 inside matter, 340–342 Lorentz force law, 210–223, 241, infinite plane, 235 with magnetic monopoles, 375, 378, 545, 568, 573 infinite solenoid, 229, 236, 337–338 in potential form, 442–444 240, 259 tensor form, 567 Lorentz gauge, 441 infinite straight line, Meissner effect, 346–347 Lorentz-Lorenz equation, 208 225–226, 229–230, 235 Merzbacher’s puzzle, 346 Lorentz transformation, magnetized object, Method. See Images; Relaxation; 519–526, 570–571 274–275, 279 Separation of variables Lorenz gauge, 440–442, 448, solenoid filled with Michelson-Morley experiment, 464, 570 magnetic material, 286 505–506 sphere of linear material in Microscopic field, 179–181, 279 Macroscopic field, 179–181, external field, 287 Minkowski, H., 530, 573 199, 279 spinning sphere, 246–247, Minkowski diagram, 529 Madelung constant, 94 249, 263–264 Minkowski force, 545, 549, 568, Magnet, 276, 284 toroidal coil, 238–239 571 Magnetic field, 210–212, 282, uniformly magnetized Minkowski’s formula, 382 550–552. See also cylinder, 276 mks units, xviii, 585–588 Charge; Dipole; Energy; uniformly magnetized Momentum Flux; Force: magnetic; object, 293, 299 angular, 370–373 Magnetization; Potential; uniformly magnetized canonical, 443 Susceptibility sphere, 275–276 conservation of, 366–370, 536 average over a sphere, 263–264 in superconductor, 337 in electromagnetic field, curl of, 229–234 work done by, 373–378 360–370 divergence of, 229–232 Magnetic induction, 282, in electromagnetic wave, of dynamic configurations 312–332 398–400 arbitrary charge Magnetic monopole, 241–242, 258, four-vector, 536 distribution, 450, 269, 339 hidden, 547–549 479–480 Magnetic susceptibility, 284–286 relativistic, 535–537

Index 595

Momentum density, 367–368, Parallel-plate capacitor, 75, Polarization (of a wave), 399 105–106, 190, 240, 391–393 Monochromatic wave, 394–398 553–555 circular, 393 Monopole Paramagnetism, 266–270, linear, 393 electric, 152, 154–155, 481 273–274 Polarization angle, 393 magnetic, 241–242, 252–253, 258, Past, 530 Polarization current, 340 339, 380 Path independence, 24–25, 30, Polarization vector, 392 Motional emf, 305–312, 53, 79–80 Pole (magnetic), 241–242, 269 503–504 Path integral, 24 Position-time four-vector, 525–526 Multipole expansion Permanent magnet, 276, 288–289 Position vector, 8–9 of electrostatic potential, Permeability, 224, 284–286, 288, Potential, 584. See also Scalar; 151–158 573 Vectors of magnetostatic potential, 252 of free space, 224, 285 advanced, 446 of radiation fields, 481 relative, 285 electric, 78–83 Mutual inductance, 321–323, Permittivity, 186, 573 in electrodynamics, 436–442 332 complex, 421 four-vector, 569–571 of free space, 60, 186 Liènard-Wiechert, 451–456, Neumann formula, 322–323 relative, 186 464 Newton’s laws Phase, 385 magnetic scalar, 249–250, 262 first law, 502 Phase constant, 385, 415 magnetic vector, 243–245, 262 Phase transition, 291 second law, 495, 542 magnetostatic scalar, 245 Phase velocity, 418 retarded, 444–448 third law, 360–362, 464, 492, Photon, 530, 538–541 Potential energy, 80 544 Pill box, 74–75 of a charge configuration, 93 Normal derivative, 90 Pinch effect, 256 of a point charge, 92 Normal incidence, reflection and Planck formula, 539 Power transmission at, 403–405 Plane dissipated in resistor, 301, 359 Normal vector, 26, 89–90, 251 of incidence, 406–407 in electromagnetic wave, 399 of polarization, 405 radiated Oblique incidence, 405–411 Plane wave, 394–398 by arbitrary source, Observer, 509 Plasma, 256 479–482 Octopole, 152, 156, 165, 482 Point charge. See Electric field; by oscillating electric Oersted, C., xv–xvi, 564 Force; Magnetic field; dipole, 471, 477 Ohm (unit), 298–299 Monopole; Potential by oscillating magnetic Ohm’s law, 296–303 Poisson’s equation, 84, 113, 244, dipole, 476 Operator, 16 284 by point charge, 482–488 Orthogonal coordinates, 575 for A, 244 Poynting vector, 358, 398–402 Orthogonal functions, 136, 144 for V, 84, 88, 113 Poynting’s theorem, 357–360 Orthogonality, 135–136, 144 Polar angle, 38 Preacceleration, 490, 492, 500 Polar molecule, 169–170 Present, 530 Paradoxes. See Barn and ladder Polarizability Pressure paradox; Ehrenfest’s atomic, 168 electromagnetic, 364 paradox; Electromagnetic tensor, 169 electrostatic, 104 paradox; Feynman disk Polarization (of a medium), 168, radiation, 400 paradox; Lorentz 172–173 Product rules, 20 contraction paradox; current, 340–341 Propagation vector, 397 Merzbacher’s puzzle; electric, 168, 172, 340–342 Pseudoscalar, 12 Time paradox; Twin induced, 168 Pseudovector, 12, 212 paradox magnetic (see Magnetization) Pulsar, 498

596 Index

Quadrupole index of, 401, 418, 422 oscillating magnetic dipole, electric, 152, 156, 165, law of, 407 473–474 481–482 Relativistic constitutive relations, point charge, arbitrary magnetic, 252 573 motion, 454 radiation, 480–481 Relativistic dynamics, 542–549 point charge, constant Quadrupole moment, 165 Relativistic electrodynamics, velocity, 454–456 Quasistatic approximation, 550–570 magnetic, 245, 249–250, 262, 319–320, 450, 451 Relativistic energy, 535–537 284 Quotient rules, 21 Relativistic kinematics, 537–542 static configurations Relativistic mass, 536 average over a sphere, Radiation, 466–501 Relativistic mechanics, 532–549 117–118 by arbitrary source, 477–482 Relativistic momentum, 535–537 conducting sphere in by electric dipole, 467–473 Relativistic potentials, 569–571 external field, 146–147 by electric quadrupole, 482 Relativity continuous charge electromagnetic, xvii, principle of, 502–508 distribution, 84–85 466–467, 482 of simultaneity, 509–510, disk, 87 by magnetic dipole, 473–477, 521–522 electric dipole, 154–155 497–499 special, xiv, 502–574 finite cylinder, 87 by point charge, 482–488 Relaxation, method of, 116 infinite line, 85–87 in hyperbolic motion, 501 Renormalization multipole expansion, by rotating electric dipole, of charge, 189–190 151–158 473–474 of mass, 495 point charges, 84–85 by surface current, 499 Resistance, 298 polarized matter, 173–176 synchrotron, 488 Resistivity, 296–297 ring, 87 Radiation damping, 490 Resistor, 297 specified charge on surface Radiation field, 460, 483 Resonant cavity, 435 of sphere, 147–148 Radiation pressure, 400 Rest energy, 536 specified electric field, 79, Radiation reaction, 488–496, Rest mass, 536 501 262 Radiation resistance, 472, 477 Retarded position, 451–454 specified potential on Radiation zone, 469, 475–476, potentials, 444–448 surface of sphere, 479 Retarded position time, 445 143–144 Rapidity, 528 Reversion of series, 494 spherical shell, 82, 86, 149 RC circuit, 302 Right hand rule, 3 surface charge, 85 Reference point Right-handed coordinates, 6 uniformly charged object, for electric dipole, 157–158 RL circuit, 331 293 for magnetic dipole, 254 Rodrigues formula, 142, 149 uniformly charged sphere, for potential, 79, 81, 83 Rotation, 10 83, 88 Reflection, 403–411 Rotation matrix, 11 uniformly polarized sphere, angle of, 407 Runaway motion, 490, 492 174–175, 178–179 at conducting surface, volume charge, 85 416–417 Saturation, 289 Scalar product, 2, 5, 7, 526–528 internal, 433 Scalar, 1 Second derivative, 22–23 law of, 407 Scalar potential, 53, 436–464 Second-rank tensor, 11–12, waves on a string, 388–391 dynamic configurations 562–563 Reflection coefficient, 405, 411 arbitrary charge Self-force, 492–496 Refraction, 403–411 distribution, 445, 479 Self-inductance, 324–327, 331 angle of, 407 oscillating electric dipole, Semiconductor, 297 coefficient of, 424 469 Separation of variables, 130–150

Index 597

Cartesian coordinates, Sunset, redness of, 472 Thomson’s dipole, 380 130–141 Superconductor, 346 Three-dimensional wave cylindrical coordinates, 150 Superluminal velocity, 418, equation, 394 spherical coordinates, 510 Threshold, 571 141–150 Superposition principle, 59, 82, Time Separation vector, xii, 9, 15, 60 97, 162 advanced, 446 Shears, 364 Surface charge, 63, 103–104, proper, 532–535 Shielding, 190 299 retarded, 445 SI units, xviii, 585–588 Surface current, 220–221 Time constant, 302, 326, 412 Simultaneity, 509–510, 521–522 Surface element, 26, 40 Time dilation, 510–514, 521–522 Sinusoidal waves, 385–388 Surface integral, 24, 26 Time paradox, 512–514 Skin depth, 413–414 Susceptibility Time reversal, 447 Sky, blueness of, 471 complex, 421 Timelike interval, 528 Snell’s law, 407 electric, 185–186, 208 TM waves, 427 Solenoid, 229, 236–237 magnetic, 284–286, 288 Toroidal coil, 238–239, 331 Solenoidal field, 54, 249 Susceptibility tensor, 190 Torque Source charge, 9, 59, 210 Symmetric tensor, 563, 564 on electric dipole, 170–171 Source point, 9, 61 Symmetry on magnetic dipole, 266–270 Space charge, 109 for Ampère’s law, 237 Total internal reflection, 433 Spacelike interval, 528 azimuthal, 141 Transformation Spacetime, structure of, 525–532 of E, B, D,andH, 293 of angles, 518, 524 Spacetime diagram, 528–532 for Gauss’s law, 72–73 of charge and current density, Spacetime interval, 528–529 of Maxwell’s equation, 566 Special relativity, xiv, 502–574 338–339 duality, 353–354, 477 Speed Synchronization, 509–510, of electromagnetic fields, of charges in wire, 242, 300 512–513, 521–522 553–560 of light in linear medium, Synchrotron radiation, 488 of forces, 545 401–402 Galilean, 519–520, 527 of light in vacuum, 394, TE waves, 427–431 gauge, 439–440 505–506 TEM waves, 427 of lengths, 514–518, 522 of waves on a string, 384 Tensor, 11–12 Lorentz, 519–526, 570–571 Spheres antisymmetric, 562–564 of momentum and energy, defined, 51 contravariant, 565 536 terminology for, 51 covariant, 565 of velocity, 534 Spherical coordinates, 38–43 dual, 564, 573 Transformer, 350 Spherical surface, 51 field, 562–565 Translation, 12 Spherical volume, 51 polarizability, 169 Transmission coefficient, 405, Spherical wave, 432 second-rank, 11–12, 562–563 411 Standing waves, 385, 429 stress, 362–366 Transmission line, 319, 352, Stationary charge, 60, 223 susceptibility, 190 431–432 Steady current, 223 symmetric, 563–564 Transmission of waves on a Step function, 49 Terminal velocity, 311–312 string, 388–391 Stokes’ theorem, 34, 55, 56, Tesla (unit), 224, 586 Transparency, 401 580–581 Test charge, 59, 210 Transverse wave, 391–393, Stress, 364 Theta function, 49 395–396, 414 Stress tensor, 362–366 Third law, 360–362, 464, 492, Triangle diagram String, waves on, 382–393 544 electrodynamics, 463 Summation convention, 527 Thompson-Lampard theorem, electrostatics, 88 Sun, age of, 110–111 166 magnetostatics, 249, 259–261

598 Index

Triple product, 7 infinite line current, Visible range (electromagnetic Tunneling, 434, 500 248–249 spectrum), 396 Twin paradox, 513–514, infinite plane current, Volt (unit), 82 524–525 248–249 Voltmeter, 349 infinite solenoid, 247 Volume charge, 63 Uniqueness theorems, 119–124, magnetic dipole, 253–255 Volume current, 220 207, 262 magnetized material, Volume element Unit systems. See Gauss; 274–275 Cartesian, 27 Heaviside-Lorentz units; multipole expansion, curvilinear, 577 SI units 252–255 cylindrical, 43–44 Unit vectors, xii, 3–4, 9, 39, 42 specified magnetic field, spherical, 40 Cartesian, 4 262 Volume integral, 24, 27–28 curvilinear, 39, 575 spinning sphere, 245–246, cylindrical, 43 263–264 Wave equation, 382–385, normal, 89–90 uniform magnetic field, 248 393–394 A spherical, 38, 42 Vector products, 3 for , 441–442 B Units, 585–588 cross product, 3, 6 for , 393–394 E ampere, 216, 224 dot product, 2, 5 for , 393–394 coulomb, 60, 585 multiplication by scalar, 2, 5, general solution, 384–385 esu (electrostatic unit), 526–528 homogeneous, 384, 394 585–586 inhomogeneous, 442 Vector triple products, 7 farad, 105 one-dimensional, 384 Vectors, 1 gauss, 224, 586 three-dimensional, 394 addition, 1–2, 5 henry, 324 for V, 441–442 component, 5, 39 ohm, 298–299 Wave guide, 425, 428 contravariant, 526 tesla, 224, 585, 586 Wave number, 385 covariant, 526–527 volt, 82 Wave vector, 397 displacement, 1, 8–9 Universal speed of light, 506 Wavelength, 385 four, 525–528 Waves magnitude, 1 Vector area, 57, 253 complex, 387 Vector operator, 16 polarization, 392 in conductors, 412–417 Vector potential, 54, 243–245, position, 8 dispersive, 417–418 436–464 propagation, 397 electromagnetic, 382–435 direction of, 247–248 pseudovectors, 12, 212 evanescent, 434 dynamic configurations separation, xii, 9, 15, 60 in free space, 393–400 arbitrary charge subtraction, 2 guided, 425–432 see distribution, 445, 479 unit ( Unit vectors) in linear media, 401–411 See also oscillating electric dipole, Velocity. Speed longitudinal, 391–392 469 4-velocity, 532–535 monochromatic, 394 oscillating magnetic dipole, drift, 242, 300 plane, 394–398 475–476 group, 418 sinusoidal, 385–388 point charge, arbitrary ordinary, 533 spherical, 432 motion, 454–455 phase, 418 standing, 385, 429–430 point charge, constant proper, 532–535 on a string, 382–393 velocity, 454–456 wave, 418 transverse, 391–393, 395 static configurations of waves on a string, 384 velocity, 384, 394, 418 arbitrary current Velocity addition rules, 507–508, water, 424 configuration, 244–245 523–524 Work finite line current, 249 Velocity field, 460, 482 and emf, 306, 328

Index 599

and potential, 91–92 by magnetic forces, 215, in polarizing a dielectric, relativistic, 543 218–220, 373–378 197–202 Work done. See also Energy in moving a charge, 91–92 in setting up a charge against back emf, 328 in moving a dielectric, conﬁguration, 91–94 in charging a capacitor, 202–204 Work energy theorem, 543–544 106–107 in moving a wire loop, 305–308 World line, 529–530