In this post, we will look at the book Principles of Electrodynamics by A. N. Matveyev (Matveev). We have seen other books by Matveev in the past, Mechanics and Theory of Relativity, Optics, Molecular Physics, and Electricity and Magnetism.

About the book

In this book, we have a clear, concise introduction, on the intermediate level, of all the tools necessary to handle the most important problems in electrodynamics, with emphasis on the experimental basis of significant phenomena. The book is divided into three parts: Phenomenological Elec­trodynamics, Electron Theory, and the Theory of Relativity. The first two parts present Maxwell’s Equations and their consequences, first intro­ducing phenomenological parameters to describe the behavior of material media and then deriving them from a more fundamental microscopic view. Einstein, through his Theory of Relativity, made possible a beautiful uni­fication of electric and magnetic phenomena. Therefore, a discussion of the historical background which led to Einstein’s theory, its fundamental concepts, and their far-reaching consequences may be found in the last part of this text. Principles of Electrodynamics, then, fills the need for a somewhat more advanced text on electricity and magnetism which does not assume great mathematical sophistication, but which does emphasize the basic physics.

The book was translated from the Russian by Leon F. Landovitz and was publised by Reinhold in 1966. AFAIK there is no translation of the book in Mir.

PDF | 440 Pg | Bookmarked | OCR

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Contents

PART I
PHENOMENOLOGICAL ELECTRODYNAMICS

1. Maxwell’s Equations as a Generalization of Experimental Fact 5

§1. The electromagnetic field. System of units 5
§2. Differential form of Gauss’ theorem 9
§3. Ohm’s law and the Joule-Lenz law in differential form 13
§4. Equation of continuity and displacement current 15
§5. Generalization of the law of total current 18
§6. Differential form of the law of electromagnetic induction 21
§7. Maxwell’s equation, div B = 0 22
§8. Maxwell’s system of equations. The energy of the electromagnetic field 23
§9. Boundary conditions 26
Problems 32

2. Electrostatics 36

§10. Possibility of considering electrical and magnetic problems separately 36
§11. Electrostatic field in a homogeneous medium 36
§12. Laplace’s equation and Poisson’s equation 41
§13. Conductors in an electrostatic field 45
§14. Dielectrics in an electrostatic field 57
§15. Energy of the electrostatic field and the energy of the interaction between charges 64
§16. Mechanical energy in an electrostatic field Problems 74
Problems 74

3. Static Magnetic Field 83

§17. General properties and equations of the magnetostatic field 83
§18. Applied emf’s and the generalized Ohm’s and Joule-Lenz laws 84
§19. Magnetostatic field in a homogeneous medium. Biot-Savart law 87
§20. Magnetic substances in a magnetic field 94
§21. Energy of the magnetic field of steady currents
§22. Mechanical forces in the magnetostatic field 105
Problems 109

4. Quasi-Static Electromagnetic Fields 117

§23. Definitions and equations 117
§24. System of conductors, taking mutual inductance and self-inductance into account 121
§25. Electric circuit with capacitance and inductance 124
§26. Induction of currents in moving conductors
§27. Skin effect 131
Problems 135

5. Generation of Electromagnetic Waves 138

§28. General equations 138
§29. Radiation of a linear oscillator 144
§30. Radiation of a current loop 154
§31. Directed radiation 156
Problems 156

6. Propagation of Electromagnetic Waves 158

§32. Propagation of electromagnetic waves in dielectrics 158
§33. Propagation of electromagnetic waves in conducting media 162
§34. Refraction and reflection of plane electromagnetic waves at a boundary between dielectrics 164
§35. Motion of electromagnetic waves along transmission lines 171
Problems 175

PART II
ELECTRON THEORY

7. Interaction of Charges with the Electromagnetic Field 179

§36. Fundamental equations of electron theory 179
§37. Motion of an electron in an electromagnetic damping 181
§38. Radiation of an oscillating electron. Radiation field 194
§39. Theory of the spectral line width 199
§40. Scattering of light by free electrons 203
§41. Momentum of an electromagnetic field. Pressure of light 204 Problems 207

8. Dielectrics

§42. Rarefied gases 212
§43. Dense gases, liquids, and solid dielectrics 217
§44. Theory of dispersion 221
Problems 226

9. Magnetic Substances 228

§45. Motion of electrons in atoms in an external magnetic field 228
§46. Diamagnetic substances 234
§47. Paramagnetic substances 237
§48. Remarks on ferromagnetism 239
§49. Gyromagnetic effects 240
Problems 243

10. Conductors 244

§50. Electrical conductivity of gases 244
§51. Electrical conductivity of liquids 249
§52. Electrical conductivity of metals 251
§53. Superconductivity 256
Problems 259

11. Relationship between Phenomenological Electrodynamics and Electron Theory 260

§54. Averaging of fields 260
§55. Averaging the microscopic current density 262
§56. Averaging the charge density 265

PART III
THEORY OF RELATIVITY

12. Postulate of the Constancy of the Velocity of Light 267

§57. The velocity of light 271
§58. Michelson’s experiment 276
§59. The ballistic hypothesis 280
§60. Fizeau’s experiment 281
§61. Postulate that the velocity of light is constant

13. The Principle of Relativity

§62. Frames of reference 286
§63. The principle of relativity in classical mechanics 90
§64. The principle of relativity in the special theory of relativity 294

14. The Lorentz Transformation and Its Kinematic Corollaries 296

§65. Derivation of the Lorentz transformation 296
§66. Length of a moving body 303
§67. Rate of moving clocks. Proper time 306
§68. Simultaneity 309
§69. Addition of velocities 312
Problems 314

15. Mathematical Apparatus of the Theory of Relativity 316

§70. Four-dimensional space 316
§71. Four-dimensional vectors 320
§72. Four-dimensional tensors 323
§73. Tensor analysis 325
§74. Tensor calculus as a tool of the theory of relativity 327

16. Relativistic Electrodynamics 329

§75. Four-dimensional potential and four-dimensional current density 329
§76. Tensor form of Maxwell’s equations 331
§77. Electromagnetic field tensors 334
§78. Four-dimensional force density 338
§79. Electromagnetic field energy momentum tensor 340
§80. Doppler effect 344
§81. Plane waves 347
§82. Field of an arbitrarily moving electron 351
§83. Electrodynamics of moving media 359
Problem 364

17. Relativistic Mechanics 365

§84. Equations of motion 365
§85. Dependence of mass on velocity 367
§86. Relationship between mass and energy 369
§87. Laws of conservation 375
§88. Charged particle accelerators 376
Problems 392

Appendix 1. Vector Algebra and Analysis Formulas Used in This Book 398
Appendix 2. International (SI) System of Units 400
Index 403