Classical Electromagnetic Theory

Classical Electromagnetic Theory......Page 3
Preface......Page 5
Table of Contents......Page 8
1.1 Static Charges......Page 14
1.2 Moving Charges......Page 26
Exercises and Problems......Page 43
2.1 Multipole Moments......Page 45
2.2 Interactions with the Field......Page 54
2.3 Potential Energy......Page 57
Exercises and Problems......Page 59
3.1 Magnetic Induction......Page 61
3.2 Displacement Current......Page 66
3.3 Maxwell’s Equations......Page 69
3.4 The Potentials......Page 70
3.5 The Wave Equation in Vacuum......Page 74
Exercises and Problems......Page 79
4.1 Energy of a Charge Distribution......Page 81
4.2 Poynting’s Theorem......Page 92
4.3 Momentum of the Fields......Page 94
4.4 Magnetic Monopoles......Page 100
4.5 Duality Transformations......Page 101
Exercises and Problems......Page 103
5.1 Laplace’s Equation......Page 105
5.2 ∇2V = 0 in Two Dimensions......Page 107
5.3 ∇2V = 0 in Three Dimensions......Page 140
Exercises and Problems......Page 151
6.1 Poisson’s Equation......Page 154
6.2 Image Charges......Page 155
6.3 Green’s Functions......Page 163
Exercises and Problems......Page 174
7.1 The Electric Field Due to a Polarized Dielectric......Page 176
7.2 Magnetic Induction Field Due to a Magnetized Material......Page 182
7.3 Microscopic Properties of Matter......Page 186
7.4 Boundary Conditions for the Static Fields......Page 192
7.5 Electrostatics and Magnetostatics in Linear Media......Page 196
7.6 Conduction in Homogeneous Matter......Page 212
7.7 Magnetic Circuits......Page 213
Exercises and Problems......Page 219
8.1 Maxwell’s Equations......Page 222
8.2 Energy and Momentum in the Fields......Page 227
8.3 The Electromagnetic Potentials......Page 232
8.4 Plane Waves in Material Media......Page 233
Exercises and Problems......Page 252
9.1 Bounded Waves......Page 254
9.2 Cylindrical Waveguides......Page 257
9.3 Dielectric Waveguides (Optical Fibers)......Page 270
Exercises and Problems......Page 277
10.1 The Inhomogeneous Wave Equation......Page 279
10.2 Radiation from a Localized Oscillating Source......Page 284
10.3 The Lienard-Wiechert Potentials......Page 304
10.4 Differentiating the Potentials......Page 315
Exercises and Problems......Page 320
11.0 Covariance......Page 322
11.1 The Four-Potential and Coulomb’s Law......Page 323
11.2 The Electromagnetic Field Tensor......Page 325
11.3 Invariants......Page 328
11.4 The Stress-Energy-Momentum Tensor......Page 329
11.5 Radiation from Relativistic Particles......Page 334
Exercises and Problems......Page 337
12.1 Electromagnetic Inertia......Page 339
12.2 The Reaction Force Needed to Conserve Energy......Page 341
12.3 Direct Calculation of Radiation Reaction: The Abraham-Lorentz Model......Page 343
12.4 The Equation of Motion......Page 346
12.5 The Covariant Equation of Motion......Page 347
12.6 Alternative Formulations......Page 348
Exercises and Problems......Page 350
Appendix A Other Systems of Units......Page 351
A.1 ESU and EMU Systems......Page 352
A.2 Gaussian Units......Page 353
B.1 Vectors......Page 355
B.2 Tensors......Page 361
B.3 Vector Identities......Page 366
B.4 Curvilinear Coordinates......Page 368
B.5 Four-Tensors in Special Relativity......Page 377
Exercises and Problems......Page 380
C.1 The Dirac Delta Function......Page 381
D.1 Orthogonal Functions......Page 385
E.1 Properties of Bessel Functions......Page 391
E.2 Related Functions......Page 395
E.3 Solution of Bessel’s Equation......Page 396
F.1 Legendre Functions......Page 401
F.2 Spherical Harmonics......Page 404
F.3 Solution of the Legendre Equation......Page 405
Appendix G Table of Symbols......Page 411
Index......Page 413
Fundamental Theories of Physics......Page 420