This book deals with electromagnetic theory and its applications at the level of a senior-level undergraduate course for science and engineering. The basic concepts and mathematical analysis are clearly developed and the important applications are analyzed. Each chapter contains numerous problems ranging in difficulty from simple applications to challenging. The answers for the problems are given at the end of the book. Some chapters which open doors to more advanced topics, such as wave theory, special relativity, emission of radiation by charges and antennas, are included.
The material of this book allows flexibility in the choice of the topics covered. Knowledge of basic calculus (vectors, differential equations and integration) and general physics is assumed. The required mathematical techniques are gradually introduced. After a detailed revision of time-independent phenomena in electrostatics and magnetism in vacuum, the electric and magnetic properties of matter are discussed. Induction, Maxwell equations and electromagnetic waves, their reflection, refraction, interference and diffraction are also studied in some detail. Four additional topics are introduced: guided waves, relativistic electrodynamics, particles in an electromagnetic field and emission of radiation. A useful appendix on mathematics, units and physical constants is included.
Contents
1. Prologue.
2. Electrostatics in Vacuum.
3. Conductors and Currents.
4. Dielectrics.
5. Special Techniques and Approximation Methods.
6. Magnetic Field in Vacuum.
7. Magnetism in Matter.
8. Induction.
9. Maxwell’s Equations.
10. Electromagnetic Waves.
11. Reflection, Interference, Diffraction and Diffusion.
12. Guided Waves.
13. Special Relativity and Electrodynamics.
14. Motion of Charged Particles in an Electromagnetic Field.
15. Emission of Radiation.
Table of Contents
Preface xi
List of Symbols xv
Chapter 1. Prologue 1
1.1. Scalars and vectors 2
1.2. Effect of rotations on scalars and vectors 5
1.3. Integrals involving vectors 7
1.4. Gradient and curl, conservative field and scalar potential 8
1.5. Divergence, conservative flux, and vector potential 10
1.6. Other properties of the vector differential operator 10
1.7. Invariance and physical laws 11
1.8. Electric charges in nature 14
1.9. Interactions in nature 18
1.10. Problems 19
Chapter 2. Electrostatics in Vacuum 23
2.1. Electric forces and field 23
2.2. Electric energy and potential 25
2.3. The two fundamental laws of electrostatics 26
2.4. Poisson’s equation and its solutions 29
2.5. Symmetries of the electric field and potential 31
2.6. Electric dipole 34
2.7. Electric field and potential of simple charge configurations 38
2.8. Some general properties of the electric field and potential 39
2.9. Electrostatic energy of a system of charges 42
2.10. Electrostatic binding energy of ionic crystals and atomic nuclei 48
2.11. Interaction-at-a-distance and local interaction* 50
2.12. Problems 52
Chapter 3. Conductors and Currents 61
3.1. Conductors in equilibrium 61
3.2. Conductors with cavities, electric shielding 64
3.3. Capacitors 66
3.4. Mutual electric influence of conductors 72
3.5. Electric forces between conductors 73
3.6. Currents and current densities 76
3.7. Classical model of conduction, Ohm’s law and the Joule effect 79
3.8. Resistance of conductors 81
3.9. Variation of resistivity with temperature, superconductivity 82
3.10. Band theory of conduction, semiconductors* 84
3.11. Electric circuits 90
3.12. Problems 92
Chapter 4. Dielectrics 97
4.1. Effects of dielectric on capacitors 97
4.2. Polarization of dielectrics 99
4.3. Microscopic interpretation of polarization 100
4.4. Polarization charges in dielectric 102
4.5. Potential and field of polarized dielectrics 103
4.6. Gauss’s law in the case of dielectrics, electric displacement 105
4.7. Electrostatic equations in dielectrics 106
4.8. Field and potential of permanent dielectrics 109
4.9. Polarization of a dielectric in an external field 113
4.10. Energy and force in dielectrics 115
4.11. Action of an electric field on a polarized medium 116
4.12. Electric susceptibility and permittivity 118
4.13. Variation of polarization with temperature 120
4.14. Nonlinear dielectrics and non-isotropic dielectrics 122
4.15. Problems 124
Chapter 5. Special Techniques and Approximation Methods 127
5.1. Unicity of the solution 128
5.2. Method of images 130
5.3. Method of analytic functions 134
5.4. Method of separation of variables 135
5.5. Laplace’s equation in Cartesian coordinates 136
5.6. Laplace’s equation in spherical coordinates 138
5.7. Laplace’s equation in cylindrical coordinates143
5.8. Multipole expansion 146
5.9. Other methods 147
5.10. Problems 149
Chapter 6. Magnetic Field in Vacuum 153
6.1. Force exerted by a magnetic field on a moving charge 153
6.2. Force exerted by a magnetic field on a current, Laplace’s force 155
6.3. Magnetic flux and vector potential 157
6.4. Magnetic field of particles and currents, Biot-Savart’s law 159
6.5. Magnetic moment 161
6.6. Symmetries of the magnetic field 165
6.7. Ampère’s law in the integral form 167
6.8. Field and potential of some simple circuits 169
6.9. Equations of time-independent magnetism in vacuum, singularities of B 174
6.10. Magnetic energy of a circuit in a field B 178
6.11. Magnetic forces 180
6.12. Question of magnetic monopoles* 186
6.13. Problems188
Chapter 7. Magnetism in Matter 195
7.1. Types of magnetism 195
7.2. Diamagnetism and paramagnetism 197
7.3. Magnetization current 201
7.4. Magnetic field and vector potential in the presence of magnetic matter 203
7.5. Ampère’s law in the integral form in the presence of magnetic matter 204
7.6. Equations of time-independent magnetism in the presence of matter 206
7.7. Discontinuities of the magnetic field 209
7 8. Examples of calculation of the field of permanent magnets 211
7.9. Magnetization of a body in an external field 214
7.10. Magnetic susceptibility, nonlinear mediums and non-isotropic mediums 216
7.11. Action of a magnetic field on a magnetic body 218
7.12. Magnetic energy in matter 220
7.13. Variation of magnetization with temperature 221
7.14. Ferromagnetism 224
7.15. Magnetic circuits 227
7.16. Problems 229
Chapter 8. Induction 233
8.1. Induction due to the variation of the flux, Faraday’s and Lenz’s laws 233
8.2. Neumann’s induction 235
8.3. Lorentz induction 236
8.4. Lorentz induction and the Galilean transformation of fields 239
8.5. Mutual inductance and self-inductance 240
8.6. LR circuit 244
8.7. Magnetic energy 247
8.8. Magnetic forces acting on circuits 249
8.9. Some applications of induction 252
8.10. Problems 256
Chapter 9. Maxwell’s Equations 263
9.1. Fundamental laws of electromagnetism 263
9.2. Maxwell’s equations 267
9.3. Electromagnetic potentials and gauge transformation 270
9.4. Quasi-permanent approximation 272
9.5. Discontinuities on the interface of two mediums 276
9.6. Electromagnetic energy and Poynting vector 277
9.7. Electromagnetic pressure, Maxwell’s tensor 278
9.8. Problems 280
Chapter 10. Electromagnetic Waves 283
10.1. A short review on waves 284
10.2. Electromagnetic waves in infinite vacuum and dielectrics 291
10.3. Polarization of electromagnetic waves 295
10.4. Energy and intensity of plane electromagnetic waves 299
10.5. Momentum and angular momentum densities, radiation pressure 301
10.6. A simple model of dispersion 304
10.7. Electromagnetic waves in conductors 308
10.8. Electromagnetic waves in plasmas 314
10.9. Quantization of electromagnetic waves 320
10.10. Electromagnetic spectrum 321
10.11. Emission of electromagnetic radiations 323
10.12. Spontaneous and stimulated emissions 325
10.13. Problems 328
Chapter 11. Reflection, Interference, Diffraction and Diffusion 337
11.1. General laws of reflection and refraction 337
11.2. Reflection and refraction on the interface of two dielectrics 340
11.3. Total reflection 346
11.4. Reflection on a conductor 349
11.5. Reflection on a plasma 352
11.6. Interference of two electromagnetic waves 353
11.7. Superposition of several waves, conditions for observable interference 355
11.8. Huygens-Fresnel’s principle and diffraction by an aperture 357
11.9. Diffraction by an obstacle, Babinet’s theorem 363
11.10. Diffraction by several randomly distributed identical apertures 364
11.11. Diffraction grating 365
11.12. X-ray diffraction 368
11.13. Diffusion of waves* 370
11.14. Cross-section* 375
11.15. Problems 378
Chapter 12. Guided Waves 389
12.1. Transmission lines 390
12.2. Guided waves 394
12.3. Waveguides formed by two plane and parallel plates 397
12.4. Guided electromagnetic waves in a hollow conductor 400
12.5. Energy propagation in waveguides 404
12.6. Cavities 406
12.7. Applications of waveguides 407
12.8. Problems 409
Chapter 13. Special Relativity and Electrodynamics 413
13.1. Galilean relativity in mechanics 414
13.2. Galilean relativity and wave theory* 415
13.3. The 19th Century experiments on the velocity of light 420
13.4. Special theory of relativity 421
13.5. Four-dimensional formalism 424
13.6. Elements of relativistic mechanics 427
13.7. Special relativity and wave theory* 430
13.8. Elements of relativistic electrodynamics 434
13.9. Problems 438
Chapter 14. Motion of Charged Particles in an Electromagnetic Field 443
14.1. Motion of a charged particle in an electric field 443
14.2. Bohr model for the hydrogen atom* 447
14.3. Rutherford’s scattering * 450
14.4. Motion of a charged particle in a magnetic field 451
14.5. Motion in crossed electric and magnetic fields 457
14.6. Magnetic moment in a magnetic field 459
14.7. Problems 461
Chapter 15. Emission of Radiation 467
15.1. Retarded potentials and fields 467
15.2. Dipole radiation 469
15.3. Electric dipole radiation 470
15.4. Magnetic dipole radiation 474
15.5. Antennas 476
15.6. Potentials and fields of a charged particle* 479
15.7. Case of a charged particle with constant velocity * 482
15.8. Radiated energy by a moving charge 484
15.9. Problems 486
Answers to Some Problems 491
Appendix A. Mathematical Review 511
Appendix B. Units in Physics 527
Appendix C. Some Physical Constants 533
Further Reading 535
Index 537
