Classical Electromagnetic Theory

This book has come into being as a result of scientific debates. And these debates have determined its structure. The first chapter is in the form of Socratic dialogues between a mathematician (MATH.), two physicists (pHYS. and EXP.) and a philosopher (PHIL.). However, although one of the authors is a theoretical physicist and the other a mathematician, the reader must not think that their opinions have been divided among the participants of the dialogues. We have tried to convey the inner tension of the topic under discussion and its openness. The attitudes of the participants reflect more the possible evaluations of the situation rather than the actual views of the authors. What is more, the subject "elementary particles" as dealt with in the 3 6 dialogue stretches over (2-3) 10 years of historical time and a space of 10 1 pages of scientific literature. For this reason, a complete survey of it is un achievable. But, of course, every researcher constructs his own history of his science and sees a certain list of its main pOints. We have attempted to float several possible pictures of this kind. Therefore the fact that Math and Phys talk about the history of element ary particles is not an attempt to present the scientific history of this realm of physics. 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