Electrodynamics | Yu. V. Novozhilov, Yu. A. Yappa.

This book originated from our experience in teaching electrodynamics as part of a series of lectures in theoretical physics. The lectures were read at the Leningrad State University for all students of the physics faculty, both future theoreticians and experimenters. The subject matter follows from what the students learned about electricity and magnetism in the general physics course, On the other hand, an electrodynamics course must serve as the basis for many special disciplines, such as plasma physics, propagation of radio-waves, electromagnetic methods in geophysics, the accelerator theory, and others. These factors have determined the content of this book and the manner of presentation.
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In accordance with the purpose of this book, we assume that the mathematical grounding corresponds to that of a student who has completed his second year in the physics faculty of a university. This should be sufficient to understand all of the material of the book. The Appendices contain the basic facts about vector and tensor analyses, which are used throughout the book, and also some properties of the Dirac delta function.

Particular attention is paid to the application of the special theory of relativity, In Chapter 2 we briefly consider the fundamentals of special relativity, while in other sections of the book we apply this theory to specific problems. Notably, the relativistic theory of radiation by a point charge is treated in great detail. The reader more interested in non-relativistic aspects of electrodynamics can skip these sections, which are marked with asterisks.

To keep the size of the book within limits we have found it necessary to exclude the specific problems of mathematical physics that originate in electrodynamics. For the same reason the book contains no exercises. The reader can find appropriate problems on classical electrodynamics in the well-known book by V. V. Batygin and I. N. Toptygin: Problems in Electrodynamics (2nd edition, Academic Press, New York, 1978). We should also like to note that the presentation is concise and hence the material requires attentive reading. The reader is advised to do all the intermediate calculations himself.

In style and subject matter this book reflects the pedagogical principles of our teacher, Academician Vladimir A. Fock, to whom it is dedicated.

The book was translated from the Russian by V. I. Kisin and was first published by Mir Publishers in 1981, and was reprinted in 1986.

Contents

Preface to the Russian Edition 7
Preface to the English Edition 9
Notation 10

Chapter 1.
The Basics of Maxwell's Electrodynamics

§ 1. The Maxwell equations. Electromagnetic units 13
§ 2. The potentials of the electromagnetic field. Gauge invariance. Hertz vectors 13
§ 3. Laws governing the variation of energy, momentum; and angular momentum 27
§ 4. Properties of the Maxwell equations. Uniqueness of the solution 33
in bounded regions. Boundary conditions at the interface between two media 38

Chapter 2.
Relativistic Electrodynamics 45

§ 5. The principle of relativity. Lorentz transformations, and
relativistic kinematics 45
§ 6. Relativistic particle dynamics 55
§ 7. The relativistic Maxwell equations. The field strength
transformations 59
§ 8. Relativistic equations of charge motion 69
§ 9*. Variational principle for electromagnetic field 75
§ 10*. The Noether theorem. Relativistic differential and integral conservation laws for electromagnetic fields 81

Chapter 3.
Static Fields. Solution of the Wave Equation. Radiation Field 90

§ 11. Electrostatic field 90
§ 12. Magnetostatic field generated by currents 98
§ 13. Solution of the nonhomogeneous wave equation. The Lienard-Wiechert potentials 103
§ 14. Field strength around a pointlike charge. Radiation
field. Uniform linear motion of a charge 110
§ 15*. Relativistic law of energy-momentum conservation for the electromagnetic field of a pointlike charge 116
§ 16. Energy radiated by a moving charge 123
§ 17. Emission from bounded oscillating sources 131

Chapter 4.
Properties of Radiation in Isotropic Media 139

§ 18. Plane waves. Reflection and refraction. Interference 139
§ 19. Relativistic transformations of plane waves 146
§ 20. Huygens principle. Fundamentals of the theory of diffraction 152
§ 21. Geometrical optics approximation 159
§ 22. Fundamentals of radiation thermodynamics 164

Chapter 5.
The Lorentz-Dirac Equation. Scattering, and Absorption of Electromagnetic Field 175

§ 23. The Lorentz-Dirac equation. Radiative reaction 175
§ 24*. Renormalization of mass. Hyperbolic motion of charge 179
§ 25. Spectrum composition of radiation emitted by an
oscillator. Scattering and absorption of radiation 183

Chapter 6.
Motion of Charged particles In Electromagnetic Field. Systems of Interacting Charges 194

§ 26. Integration of the equations of motion 194
§ 27. Theory of drift in nonuniform electromagnetic fields 206
§ 28. Systems of interacting particles 214

Chapter 7. Continuous Media In Electric Field 225

§ 29. Introduction to electrodynamics of continuous media 225
§ 30. Ideal conductors in electrostatic field 228
§ 31. Dielectrics in electrostatic field. Isotropic dielectrics 236
§ 32. Anisotropic dielectrics 249

Chapter 8. Electric Current. Magnetic Field in Continuous Media 254

§ 33. Magnetic energy and forces in a system of direct-current loops.
Quasistationary currents in linear circuits 254
§ 34. Eddy currents. Thermoelectric and thermomagnetic pheno-
mena. Hall effect 263
§ 35. Elements of magnetohydrodynamics 270
§ 36. Elementary properties of ferromagnetics 277
§ 37. Phenomenological description of superconductivity 288

Chapter 9.
Alternating Electromagnetic Field In Continuous Media 295

§ 38. Electromagnetic waves in conductors. Waveguide and cavity 295
§ 39. Dispersion of electromagnetic field' in the medium. Waves in anisotropic media 301
§ 40. Waves in magnetohydrodynamics 313
§ 41. Fundamentals of nonlinear optics 318

Appendix 322

A. Basic formulas of tensor analysis 322
B. Vector analysis in three-dimensional Euclidean space 328
C. Basic formulas for delta function and its derivatives 334
D. Integration over hypersurfaces in the Minkowski space 336
E. Application of the Fourier transform to wave equations 341

Name Index 346
Subject Index 348