Modern electrodynamics

Modern Electrodynamics......Page 1
Contents......Page 7
List of Applications......Page 15
Preface......Page 19
1.2 Vectors......Page 23
1.3 Derivatives......Page 29
1.4 Integrals......Page 31
1.5 Generalized Functions......Page 33
1.6 Fourier Analysis......Page 37
1.7 Orthogonal Transformations......Page 40
1.8 Cartesian Tensors......Page 42
1.9 The Helmholtz Theorem......Page 44
Sources, References, and Additional Reading......Page 46
Problems......Page 47
2.1 Introduction......Page 51
2.2 The Maxwell Equations in Vacuum......Page 55
2.3 Microscopic vs. Macroscopic......Page 60
2.4 The Maxwell Equations in Matter......Page 65
2.5 Quantum Limits and New Physics......Page 68
2.6 SI Units......Page 72
2.7 A Heuristic Derivation......Page 73
Sources, References, and Additional Reading......Page 75
Problems......Page 77
3.1 Introduction......Page 80
3.2 Coulomb’s Law......Page 81
3.3 The Scalar Potential......Page 82
3.4 Gauss’ Law and Solid Angle......Page 90
3.5 Electrostatic Potential Energy......Page 96
3.6 Electrostatic Total Energy......Page 98
3.7 The Electric Stress Tensor......Page 103
Sources, References, and Additional Reading......Page 106
Problems......Page 107
4.1 Introduction......Page 112
4.2 The Electric Dipole......Page 114
4.3 Electric Dipole Layers......Page 120
4.4 The Electric Quadrupole......Page 124
4.5 Spherical Mathematics......Page 128
4.6 Spherical and Azimuthal Multipoles......Page 131
4.7 Primitive and Traceless Multipole Moments......Page 138
Sources, References, and Additional Reading......Page 141
Problems......Page 143
5.2 Electrostatic Induction......Page 148
5.3 Screening and Shielding......Page 155
5.4 Capacitance......Page 156
5.5 The Energy of a System of Conductors......Page 164
5.6 Forces on Conductors......Page 165
5.7 Real Conductors......Page 171
Sources, References, and Additional Reading......Page 173
Problems......Page 174
6.2 Polarization......Page 180
6.3 The Field Produced by Polarized Matter......Page 184
6.4 The Total Electric Field......Page 187
6.5 Simple Dielectric Matter......Page 189
6.6 The Physics of the Dielectric Constant......Page 197
6.7 The Energy of Dielectric Matter......Page 200
6.8 Forces on Dielectric Matter......Page 206
Sources, References, and Additional Reading......Page 213
Problems......Page 215
7.1 Introduction......Page 219
7.2 Potential Theory......Page 220
7.3 Uniqueness......Page 221
7.4 Separation of Variables......Page 223
7.5 Cartesian Symmetry......Page 225
7.6 Azimuthal Symmetry......Page 231
7.7 Spherical Symmetry......Page 234
7.8 Cylindrical Symmetry......Page 237
7.9 Polar Coordinates......Page 240
7.10 The Complex Potential......Page 243
7.11 A Variational Principle......Page 248
Sources, References, and Additional Reading......Page 250
Problems......Page 251
8.2 The Key Idea: Superposition......Page 258
8.3 The Method of Images......Page 259
8.4 The Green Function Method......Page 272
8.5 The Dirichlet Green Function......Page 274
8.6 The Complex Logarithm Potential......Page 282
8.7 The Poisson-Boltzmann Equation......Page 284
Sources, References, and Additional Reading......Page 286
Problems......Page 287
9.1 Introduction......Page 294
9.2 Current in Vacuum......Page 295
9.3 Current in Matter......Page 297
9.4 Potential Theory for Ohmic Matter......Page 298
9.5 Electrical Resistance......Page 299
9.6 Joule Heating......Page 302
9.7 Electromotive Force......Page 304
9.8 Current Sources......Page 309
9.9 Diffusion Current: Fick’s Law......Page 313
Sources, References, and Additional Reading......Page 315
Problems......Page 316
10.1 Introduction......Page 323
10.2 The Law of Biot and Savart......Page 326
10.3 Amp`ere’s Law......Page 329
10.4 The Magnetic Scalar Potential......Page 334
10.5 The Vector Potential......Page 342
10.6 The Topology of Magnetic Field Lines......Page 347
Sources, References, and Additional Reading......Page 351
Problems......Page 352
11.1 Introduction......Page 358
11.2 The Magnetic Dipole......Page 359
11.3 Magnetic Dipole Layers......Page 367
11.4 Exterior Multipoles......Page 368
11.5 Interior Multipoles......Page 375
11.6 Axially Symmetric Magnetic Fields......Page 379
Sources, References, and Additional Reading......Page 381
Problems......Page 383
12.1 Introduction......Page 387
12.2 Charged Particle Motion......Page 388
12.3 The Force between Steady Currents......Page 390
12.4 The Magnetic Dipole......Page 394
12.5 The Magnetic Stress Tensor......Page 403
12.6 Magnetostatic Total Energy......Page 406
12.7 Magnetostatic Potential Energy......Page 411
12.8 Inductance......Page 416
Sources, References, and Additional Reading......Page 421
Problems......Page 423
13.2 Magnetization......Page 429
13.3 The Field Produced by Magnetized Matter......Page 434
13.4 Fictitious Magnetic Charge......Page 437
13.5 The Total Magnetic Field......Page 441
13.6 Simple Magnetic Matter......Page 443
13.7 The Energy of Magnetic Matter......Page 455
13.8 Forces on Magnetic Matter......Page 457
13.9 Permanent Magnetic Matter......Page 465
Sources, References, and Additional Reading......Page 469
Problems......Page 470
14.1 Introduction......Page 477
14.2 The Amp`ere-Maxwell Law......Page 478
14.3 Faraday’s Law......Page 482
14.4 Electromagnetic Induction......Page 484
14.5 Slowly Time-Varying Charge in Vacuum......Page 489
14.6 Slowly Time-Varying Current in Vacuum......Page 492
14.7 Quasistatic Fields in Matter......Page 494
14.8 Poor Conductors: Quasi-Electrostatics......Page 495
14.9 Good Conductors: Quasi-Magnetostatics......Page 497
14.10 The Skin Effect......Page 499
14.11 Magnetic Diffusion......Page 503
14.12 Eddy-Current Phenomena......Page 505
14.13 AC Circuit Theory......Page 508
Sources, References, and Additional Reading......Page 515
Problems......Page 516
15.2 Symmetry......Page 523
15.3 Electromagnetic Potentials......Page 525
15.4 Conservation of Energy......Page 529
15.5 Conservation of Linear Momentum......Page 533
15.6 Conservation of Angular Momentum......Page 538
15.7 The Center of Energy......Page 541
15.8 Conservation Laws in Matter......Page 544
15.9 The Force on Isolated Matter......Page 548
Sources, References, and Additional Reading......Page 551
Problems......Page 553
16.1 Introduction......Page 558
16.2 The Wave Equation......Page 559
16.3 Plane Waves......Page 561
16.4 Polarization......Page 567
16.5 Wave Packets......Page 574
16.6 The Helmholtz Equation......Page 579
16.7 Beam-Like Waves......Page 580
16.8 Spherical Waves......Page 587
16.9 Hertz Vectors......Page 591
16.10 Forces on Particles in Free Fields......Page 593
Sources, References, and Additional Reading......Page 597
Problems......Page 599
17.2 Plane Waves......Page 606
17.3 Reflection and Refraction......Page 610
17.4 Radiation Pressure......Page 621
17.5 Layered Matter......Page 624
17.6 Simple Conducting Matter......Page 629
17.7 Anisotropic Matter......Page 635
Sources, References, and Additional Reading......Page 638
Problems......Page 639
18.2 Frequency Dispersion......Page 646
18.3 Energy in Dispersive Matter......Page 649
18.4 Transverse and Longitudinal Waves......Page 651
18.5 Classical Models for Frequency Dispersion......Page 652
18.6 Wave Packets in Dispersive Matter......Page 663
18.7 The Consequences of Causality......Page 671
18.8 Spatial Dispersion......Page 678
Sources, References, and Additional Reading......Page 679
Problems......Page 681
19.1 Introduction......Page 688
19.2 Transmission Lines......Page 689
19.3 Planar Conductors......Page 694
19.4 Conducting Tubes......Page 697
19.5 Dielectric Waveguides......Page 709
19.6 Conducting Cavities......Page 715
19.7 Dielectric Resonators......Page 726
Sources, References, and Additional Reading......Page 728
Problems......Page 729
20.1 Introduction......Page 736
20.2 Inhomogeneous Wave Equations......Page 737
20.3 Retardation......Page 741
20.4 The Time-Dependent Electric Dipole......Page 749
20.5 Radiation......Page 752
20.6 Thin-Wire Antennas......Page 759
20.7 Cartesian Multipole Radiation......Page 765
20.8 Spherical Multipole Radiation......Page 777
20.9 Radiation in Matter......Page 784
Sources, References, and Additional Reading......Page 787
Problems......Page 789
21.1 Introduction......Page 797
21.2 The Scattering Cross Section......Page 798
21.3 Thomson Scattering......Page 799
21.4 Rayleigh Scattering......Page 804
21.5 Two Exactly Solvable Problems......Page 805
21.6 Two Approximation Schemes......Page 812
21.7 The Total Cross Section......Page 815
21.8 Diffraction by a Planar Aperture......Page 819
21.9 Generalized Optical Principles......Page 829
Sources, References, and Additional Reading......Page 834
Problems......Page 836
22.1 Introduction......Page 844
22.2 Galileo’s Relativity......Page 845
22.3 Einstein’s Relativity......Page 847
22.4 The Lorentz Transformation......Page 848
22.5 Four-Vectors......Page 856
22.6 Electromagnetic Quantities......Page 861
22.7 Covariant Electrodynamics......Page 870
22.8 Matter in Uniform Motion......Page 880
Sources, References, and Additional Reading......Page 885
Problems......Page 887
23.2 The Li´enard-Wiechert Problem......Page 892
23.3 Radiation in the Time Domain......Page 902
23.4 Radiation in the Frequency Domain......Page 908
23.5 Synchrotron Radiation......Page 913
23.6 Radiation Reaction......Page 921
23.7 Cherenkov Radiation......Page 928
Sources, References, and Additional Reading......Page 932
Problems......Page 934
24.2 Hamilton’s Principle......Page 938
24.3 Lagrangian Description......Page 940
24.4 Invariance and Conservation Laws......Page 949
24.5 Hamiltonian Description......Page 953
Sources, References, and Additional Reading......Page 962
Problems......Page 963
Appendix A List of Important Symbols......Page 967
Appendix B Gaussian Units......Page 971
Appendix C Special Functions......Page 975
Appendix D Managing Minus Signs in Special Relativity......Page 981
Index......Page 986