Electromagnetism : Maxwell equations, wave propagation, and emission

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.

Author Notes

Tamer Bcherrawy received a Doctorate from the University of Paris and a PhD in theoretical physics from the University of Rochester, New York. He has taught physics at the Faculty of Science of the Lebanese University in Beirut, the University of Savoy in Chambery, the IUFM and the University of Nancy in France. He was head of the Physics Department at the Lebanese University and is the author of a number of research articles on High Energy Particle Physics.

Preface	p. xi
List of Symbols	p. xv
Chapter 1 Prologue	p. 1
1.1 Scalars and vectors	p. 2
1.2 Effect of rotations on scalars and vectors	p. 5
1.3 Integrals involving vectors	p. 7
1.4 Gradient and curl, conservative field and scalar potential	p. 8
1.5 Divergence, conservative flux, and vector potential	p. 10
1.6 Other properties of the vector differential operator	p. 10
1.7 Invariance and physical laws	p. 11
1.8 Electric charges in nature	p. 14
1.9 Interactions in nature	p. 18
1.10 Problems	p. 19
Chapter 2 Electrostatics in Vacuum	p. 23
2.1 Electric forces and field	p. 23
2.2 Electric energy and potential	p. 25
2.3 The two fundamental laws of electrostatics	p. 26
2.4 Poisson's equation and its solutions	p. 29
2.5 Symmetries of the electric field and potential	p. 31
2.6 Electric dipole	p. 34
2.7 Electric field and potential of simple charge configurations	p. 38
2.8 Some general properties of the electric field and potential	p. 39
2.9 Electrostatic energy of a system of charges	p. 42
2.10 Electrostatic binding energy of ionic crystals and atomic nuclei	p. 48
2.11 Interaction-at-a-distance and local interaction*	p. 50
2.12 Problems	p. 52
Chapter 3 Conductors and Currents	p. 61
3.1 Conductors in equilibrium	p. 61
3.2 Conductors with cavities, electric shielding	p. 64
3.3 Capacitors	p. 66
3.4 Mutual electric influence of conductors	p. 72
3.5 Electric forces between conductors	p. 73
3.6 Currents and current densities	p. 76
3.7 Classical model of conduction, Ohm's law and the Joule effect	p. 79
3.8 Resistance of conductors	p. 81
3.9 Variation of resistivity with temperature, superconductivity	p. 82
3.10 Band theory of conduction, semiconductors*	p. 84
3.11 Electric circuits	p. 90
3.12 Problems	p. 92
Chapter 4 Dielectrics	p. 97
4.1 Effects of dielectric on capacitors	p. 97
4.2 Polarization of dielectrics	p. 99
4.3 Microscopic interpretation of polarization	p. 100
4.4 Polarization charges in dielectric	p. 102
4.5 Potential and field of polarized dielectrics	p. 103
4.6 Gauss's law in the case of dielectrics, electric displacement	p. 105
4.7 Electrostatic equations in dielectrics	p. 106
4.8 Field and potential of permanent dielectrics	p. 109
4.9 Polarization of a dielectric in an external field	p. 113
4.10 Energy and force in dielectrics	p. 115
4.11 Action of an electric field on a polarized medium	p. 116
4.12 Electric susceptibility and permitivity	p. 118
4.13 Variation of polarization with temperature	p. 120
4.14 Nonlinear of dielectrics and non-isotropic dielectrics	p. 122
4.15 Problems	p. 124
Chapter 5 Special Techniques and Approximation Methods	p. 127
5.1 Unicity of the solution	p. 128
5.2 Method of images	p. 130
5.3 Method of analytic functions	p. 134
5.4 Method of separation of variables	p. 135
5.5 Laplace's equation in Cartesian coordinates	p. 136
5.6 Laplace's equation in spherical coordinates	p. 138
5.7 Laplace's equation in cylindrical coordinates	p. 143
5.8 Multipole expansion	p. 146
5.9 Other methods	p. 147
5.10 Problems	p. 149
Chapter 6 Magnetic Field in Vacuum	p. 153
6.1 Force exerted by a magnetic field on a moving charge	p. 153
6.2 Force exerted by a magnetic field on a current, Laplace's force	p. 155
6.3 Magnetic flux and vector potential	p. 157
6.4 Magnetic field of particles and currents, Biot-Savart's law	p. 159
6.5 Magnetic moment	p. 161
6.6 Symmetries of the magnetic field	p. 165
6.7 Ampère's law in the integral form	p. 167
6.8 Field and potential of some simple circuits	p. 169
6.9 Equations of time-independent magnetism in vacuum, singularities of B	p. 174
6.10 Magnetic energy of a circuit in a field B	p. 178
6.11 Magnetic forces	p. 180
6.12 Question of magnetic monopoles*	p. 186
6.13 Problems	p. 188
Chapter 7 Magnetism in Matter	p. 195
7.1 Types of magnetism	p. 195
7.2 Diamagnetism and paramagnetism	p. 197
7.3 Magnetization current	p. 201
7.4 Magnetic field and vector potential in the presence of magnetic matter	p. 203
7.5 Ampère's law in the integral form in the presence of magnetic matter	p. 204
7.6 Equations of time-independent magnetism in the presence of matter	p. 206
7.7 Discontinuities of the magnetic field	p. 209
7.8 Examples of calculation of the field of permanent magnets	p. 211
7.9 Magnetization of a body in an external field	p. 214
7.10 Magnetic susceptibility, nonlinear mediums and non-isotropic mediums	p. 216
7.11 Action of a magnetic field on a magnetic body	p. 218
7.12 Magnetic energy in matter	p. 220
7.13 Variation of magnetization with temperature	p. 221
7.14 Ferromagnetism	p. 224
7.15 Magnetic circuits	p. 227
7.16 Problems	p. 229
Chapter 8 Induction	p. 233
8.1 Induction due to the variation of the flux, Faraday's and Lenz's laws	p. 233
8.2 Neumann's induction	p. 235
8.3 Lorentz induction	p. 236
8.4 Lorentz induction and the Galilean transformation of fields	p. 239
8.5 Mutual inductance and self-inductance	p. 240
8.6 LR circuit	p. 244
8.7 Magnetic energy	p. 247
8.8 Magnetic forces acting on circuits	p. 249
8.9 Some applications of induction	p. 252
8.10 Problems	p. 256
Chapter 9 Maxwell's Equations	p. 263
9.1 Fundamental laws of electromagnetism	p. 263
9.2 Maxwell's equations	p. 267
9.3 Electromagnetic potentials and gauge transformation	p. 270
9.4 Quasi-permanent approximation	p. 272
9.5 Discontinuities on the interface of two mediums	p. 276
9.6 Electromagnetic energy and Poynting vector	p. 277
9.7 Electromagnetic pressure, Maxwell's tensor	p. 278
9.8 Problems	p. 280
Chapter 10 Electromagnetic Waves	p. 283
10.1 A short review on waves	p. 284
10.2 Electromagnetic waves in infinite vacuum and dielectrics	p. 291
10.3 Polarization of electromagnetic waves	p. 295
10.4 Energy and intensity of plane electromagnetic waves	p. 299
10.5 Momentum and angular momentum densities, radiation pressure	p. 301
10.6 A simple model of dispersion	p. 304
10.7 Electromagnetic waves in conductors	p. 308
10.8 Electromagnetic waves in plasmas	p. 314
10.9 Quantization of electromagnetic waves	p. 320
10.10 Electromagnetic spectrum	p. 321
10.11 Emission of electromagnetic radiations	p. 323
10.12 Spontaneous and stimulated emissions	p. 325
10.13 Problems	p. 328
Chapter 11 Reflection, Interference, Diffraction and Diffusion	p. 337
11.1 General laws of reflection and refraction	p. 337
11.2 Reflection and refraction on the interface of two dielectrics	p. 340
11.3 Total reflection	p. 346
11.4 Reflection on a conductor	p. 349
11.5 Reflection on a plasma	p. 352
11.6 Interference of two electromagnetic waves	p. 353
11.7 Superposition of several waves, conditions for observable interference	p. 355
11.8 Huygens-Fresnel's principle and diffraction by an aperture	p. 357
11.9 Diffraction by an obstacle, Babinet's theorem	p. 363
11.10 Diffraction by several randomly distributed identical apertures	p. 364
11.11 Diffraction grating	p. 365
11.12 X-ray diffraction	p. 368
11.13 Diffusion of waves*	p. 370
11.14 Cross-section*	p. 375
11.15 Problems	p. 378
Chapter 12 Guided Waves	p. 389
12.1 Transmission lines	p. 390
12.2 Guided waves	p. 394
12.3 Waveguides formed by two plane and parallel plates	p. 397
12.4 Guided electromagnetic waves in a hollow conductor	p. 400
12.5 Energy propagation in waveguides	p. 404
12.6 Cavities	p. 406
12.7 Applications of waveguides	p. 407
12.8 Problems	p. 409
Chapter 13 Special Relativity and Electrodynamics	p. 413
13.1 Galilean relativity in mechanics	p. 414
13.2 Galilean relativity and wave theory*	p. 415
13.3 The 19th Century experiments on the velocity of light	p. 420
13.4 Special theory of relativity	p. 421
13.5 Four-dimensional formalism	p. 424
13.6 Elements of relativistic mechanics	p. 427
13.7 Special relativity and wave theory*	p. 430
13.8 Elements of relativistic electrodynamics	p. 434
13.9 Problems	p. 438
Chapter 14 Motion of Charged Particles in an Electromagnetic Field	p. 443
14.1 Motion of a charged particle in an electric field	p. 443
14.2 Bohr model for the hydrogen atom*	p. 447
14.3 Rutherford's scattering*	p. 450
14.4 Motion of a charged particle in a magnetic field	p. 451
14.5 Motion in crossed electric and magnetic fields	p. 457
14.6 Magnetic moment in a magnetic field	p. 459
14.7 Problems	p. 461
Chapter 15 Emission of Radiation	p. 467
15.1 Retarded potentials and fields	p. 467
15.2 Dipole radiation	p. 469
15.3 Electric dipole radiation	p. 470
15.4 Magnetic dipole radiation	p. 474
15.5 Antennas	p. 476
15.6 Potentials and fields of a charged particle*	p. 479
15.7 Case of a charged particle with constant velocity*	p. 482
15.8 Radiated energy by a moving charge	p. 484
15.9 Problems	p. 486
Answers to Some Problems	p. 491
Appendix A Mathematical Review	p. 511
Appendix B Units in Physics	p. 527
Appendix C Some Physical Constants	p. 533
Further Reading	p. 535
Index	p. 537

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Author Notes

Table of Contents