Electromagnetism Maxwell Equations, Wave Propagation and Emission

by Becherrawy, Tamer

• ISBN13: 9781848213555
• ISBN10: 1848213557
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-07-16
• Publisher: Wiley-ISTE

Summary

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.

Author Biography

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.

Table of Contents

Preface	p. xi
List of Symbols	p. xv
Prologue	p. 1
Scalars and vectors	p. 2
Effect of rotations on scalars and vectors	p. 5
Integrals involving vectors	p. 7
Gradient and curl, conservative field and scalar potential	p. 8
Divergence, conservative flux, and vector potential	p. 10
Other properties of the vector differential operator	p. 10
Invariance and physical laws	p. 11
Electric charges in nature	p. 14
Interactions in nature	p. 18
Problems	p. 19
Electrostatics in Vacuum	p. 23
Electric forces and field	p. 23
Electric energy and potential	p. 25
The two fundamental laws of electrostatics	p. 26
Poisson's equation and its solutions	p. 29
Symmetries of the electric field and potential	p. 31
Electric dipole	p. 34
Electric field and potential of simple charge configurations	p. 38
Some general properties of the electric field and potential	p. 39
Electrostatic energy of a system of charges	p. 42
Electrostatic binding energy of ionic crystals and atomic nuclei	p. 48
Interaction-at-a-distance and local interaction*	p. 50
Problems	p. 52
Conductors and Currents	p. 61
Conductors in equilibrium	p. 61
Conductors with cavities, electric shielding	p. 64
Capacitors	p. 66
Mutual electric influence of conductors	p. 72
Electric forces between conductors	p. 73
Currents and current densities	p. 76
Classical model of conduction, Ohm's law and the Joule effect	p. 79
Resistance of conductors	p. 81
Variation of resistivity with temperature, superconductivity	p. 82
Band theory of conduction, semiconductors*	p. 84
Electric circuits	p. 90
Problems	p. 92
Dielectrics	p. 97
Effects of dielectric on capacitors	p. 97
Polarization of dielectrics	p. 99
Microscopic interpretation of polarization	p. 100
Polarization charges in dielectric	p. 102
Potential and field of polarized dielectrics	p. 103
Gauss's law in the case of dielectrics, electric displacement	p. 105
Electrostatic equations in dielectrics	p. 106
Field and potential of permanent dielectrics	p. 109
Polarization of a dielectric in an external field	p. 113
Energy and force in dielectrics	p. 115
Action of an electric field on a polarized medium	p. 116
Electric susceptibility and permitivity	p. 118
Variation of polarization with temperature	p. 120
Nonlinear of dielectrics and non-isotropic dielectrics	p. 122
Problems	p. 124
Special Techniques and Approximation Methods	p. 127
Unicity of the solution	p. 128
Method of images	p. 130
Method of analytic functions	p. 134
Method of separation of variables	p. 135
Laplace's equation in Cartesian coordinates	p. 136
Laplace's equation in spherical coordinates	p. 138
Laplace's equation in cylindrical coordinates	p. 143
Multipole expansion	p. 146
Other methods	p. 147
Problems	p. 149
Magnetic Field in Vacuum	p. 153
Force exerted by a magnetic field on a moving charge	p. 153
Force exerted by a magnetic field on a current, Laplace's force	p. 155
Magnetic flux and vector potential	p. 157
Magnetic field of particles and currents, Biot-Savart's law	p. 159
Magnetic moment	p. 161
Symmetries of the magnetic field	p. 165
Ampère's law in the integral form	p. 167
Field and potential of some simple circuits	p. 169
Equations of time-independent magnetism in vacuum, singularities of B	p. 174
Magnetic energy of a circuit in a field B	p. 178
Magnetic forces	p. 180
Question of magnetic monopoles*	p. 186
Problems	p. 188
Magnetism in Matter	p. 195
Types of magnetism	p. 195
Diamagnetism and paramagnetism	p. 197
Magnetization current	p. 201
Magnetic field and vector potential in the presence of magnetic matter	p. 203
Ampère's law in the integral form in the presence of magnetic matter	p. 204
Equations of time-independent magnetism in the presence of matter	p. 206
Discontinuities of the magnetic field	p. 209
Examples of calculation of the field of permanent magnets	p. 211
Magnetization of a body in an external field	p. 214
Magnetic susceptibility, nonlinear mediums and non-isotropic mediums	p. 216
Action of a magnetic field on a magnetic body	p. 218
Magnetic energy in matter	p. 220
Variation of magnetization with temperature	p. 221
Ferromagnetism	p. 224
Magnetic circuits	p. 227
Problems	p. 229
Induction	p. 233
Induction due to the variation of the flux, Faraday's and Lenz's laws	p. 233
Neumann's induction	p. 235
Lorentz induction	p. 236
Lorentz induction and the Galilean transformation of fields	p. 239
Mutual inductance and self-inductance	p. 240
LR circuit	p. 244
Magnetic energy	p. 247
Magnetic forces acting on circuits	p. 249
Some applications of induction	p. 252
Problems	p. 256
Maxwell's Equations	p. 263
Fundamental laws of electromagnetism	p. 263
Maxwell's equations	p. 267
Electromagnetic potentials and gauge transformation	p. 270
Quasi-permanent approximation	p. 272
Discontinuities on the interface of two mediums	p. 276
Electromagnetic energy and Poynting vector	p. 277
Electromagnetic pressure, Maxwell's tensor	p. 278
Problems	p. 280
Electromagnetic Waves	p. 283
A short review on waves	p. 284
Electromagnetic waves in infinite vacuum and dielectrics	p. 291
Polarization of electromagnetic waves	p. 295
Energy and intensity of plane electromagnetic waves	p. 299
Momentum and angular momentum densities, radiation pressure	p. 301
A simple model of dispersion	p. 304
Electromagnetic waves in conductors	p. 308
Electromagnetic waves in plasmas	p. 314
Quantization of electromagnetic waves	p. 320
Electromagnetic spectrum	p. 321
Emission of electromagnetic radiations	p. 323
Spontaneous and stimulated emissions	p. 325
Problems	p. 328
Reflection, Interference, Diffraction and Diffusion	p. 337
General laws of reflection and refraction	p. 337
Reflection and refraction on the interface of two dielectrics	p. 340
Total reflection	p. 346
Reflection on a conductor	p. 349
Reflection on a plasma	p. 352
Interference of two electromagnetic waves	p. 353
Superposition of several waves, conditions for observable interference	p. 355
Huygens-Fresnel's principle and diffraction by an aperture	p. 357
Diffraction by an obstacle, Babinet's theorem	p. 363
Diffraction by several randomly distributed identical apertures	p. 364
Diffraction grating	p. 365
X-ray diffraction	p. 368
Diffusion of waves*	p. 370
Cross-section*	p. 375
Problems	p. 378
Guided Waves	p. 389
Transmission lines	p. 390
Guided waves	p. 394
Waveguides formed by two plane and parallel plates	p. 397
Guided electromagnetic waves in a hollow conductor	p. 400
Energy propagation in waveguides	p. 404
Cavities	p. 406
Applications of waveguides	p. 407
Problems	p. 409
Special Relativity and Electrodynamics	p. 413
Galilean relativity in mechanics	p. 414
Galilean relativity and wave theory*	p. 415
The 19th Century experiments on the velocity of light	p. 420
Special theory of relativity	p. 421
Four-dimensional formalism	p. 424
Elements of relativistic mechanics	p. 427
Special relativity and wave theory*	p. 430
Elements of relativistic electrodynamics	p. 434
Problems	p. 438
Motion of Charged Particles in an Electromagnetic Field	p. 443
Motion of a charged particle in an electric field	p. 443
Bohr model for the hydrogen atom*	p. 447
Rutherford's scattering*	p. 450
Motion of a charged particle in a magnetic field	p. 451
Motion in crossed electric and magnetic fields	p. 457
Magnetic moment in a magnetic field	p. 459
Problems	p. 461
Emission of Radiation	p. 467
Retarded potentials and fields	p. 467
Dipole radiation	p. 469
Electric dipole radiation	p. 470
Magnetic dipole radiation	p. 474
Antennas	p. 476
Potentials and fields of a charged particle*	p. 479
Case of a charged particle with constant velocity*	p. 482
Radiated energy by a moving charge	p. 484
Problems	p. 486
Answers to Some Problems	p. 491
Mathematical Review	p. 511
Units in Physics	p. 527
Some Physical Constants	p. 533
Further Reading	p. 535
Index	p. 537
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