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.

Tamer Bécherrawy 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.

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.

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 magne…