Classical Theory of Electromagnetism,9789812382184

Classical Theory of Electromagnetism

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Edition: 2nd
ISBN13: 9789812382184
ISBN10: 9812382186
Format: Hardcover
Pub. Date: 2004-06-01
Publisher(s): World Scientific Pub Co Inc
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Summary

The topics treated in this book are essentially those that a graduate student of physics or electrical engineering should be familiar with in classical electromagnetism. Each topic is analyzed in detail, and each new concept is explained with examples.The text is self-contained and oriented toward the student. It is concise and yet very detailed in mathematical calculations; the equations are explicitly derived, which is of great help to students and allows them to concentrate more on the physics concepts, rather than spending too much time on mathematical derivations. The introduction of the theory of special relativity is always a challenge in teaching electromagnetism, and this topic is considered with particular care. The value of the book is increased by the inclusion of a large number of exercises.

Table of Contents

Foreword xv
Preface to the Second Edition xvii
Preface to the First Edition xix
Chapter 1 Mathematical Introduction 1(18)
1.1 Vector Notation
1(3)
1.2 Fields
4(1)
1.3 Vector Differential Operator
5(2)
1.4 Gauss's Theorem and Related Theorems
7(7)
1.4.1 The Gradient Theorem
8(1)
1.4.2 The Divergence Theorem
9(1)
1.4.3 The Curl Theorem
9(1)
1.4.4 Green's Theorem
10(1)
1.4.5 Stokes's Theorem
11(3)
Exercises
14(5)
Chapter 2 Charges and Electrostatics 19(90)
2.1 Basic Phenomena
19(3)
2.1.1 The Superposition Principle
20(1)
2.1.2 The Symmetry Principle
21(1)
2.2 Units
22(3)
2.2.1 The Electrostatic System of Units (ESU)
22(1)
2.2.2 The International System of Units (SI)
23(2)
2.3 The Gauss Flux Theorem and the First Maxwell Equation
25(2)
2.4 Singular and General Charge Distributions
27(5)
2.5 Some Potential Theory
32(3)
2.6 Properties of Spherical Harmonics
35(6)
2.6.1 Normalization
35(1)
2.6.2 Orthogonality
35(1)
2.6.3 Symmetry
36(1)
2.6.4 Examples
36(1)
2.6.5 Legendre Polynomials, rhoι(costheta)
36(5)
2.7 The Mean Value Theorem
41(1)
2.8 Conductors and Insulators
42(3)
2.9 General Electrostatic Problems
45(134)
2.9.1 Dirichiet Boundary Value Problem
48(1)
2.9.2 Neumann Boundary Value Problem
49(7)
2.10 Forces and the Stress Tensor
56(4)
2.11 The Field Energy
60(4)
2.12 Earnshaw's Theorem
64(2)
2.13 Thompson's Theorem
66(7)
2.14 Polarization
73(10)
2.15 Field Energy in a Dielectric with Constant Kappa
83(2)
2.16 Field Energy in a Dielectric for Which Kappa = Kappa(χ)
85(2)
2.17 Forces on a Dielectric
87(4)
2.18 The Stress Tensor
91(3)
2.19 Capacitance
94(4)
Exercises
98(11)
Chapter 3 Stationary Currents and Magnetostatics 109(48)
3.1 Lorentz Force and the Biot and Savart Law
109(7)
3.1.1 The Force Law
109(4)
3.1.2 The Biot and Savart Law
113(3)
3.2 Forces between Current Loops
116(1)
3.3 Units
117(7)
3.3.1 The Electromagnetic System of Units (EMU)
117(2)
3.3.2 The SI System of Units
119(1)
3.3.3 The Gaussian System of Units
120(4)
3.4 The Vector Potential
124(3)
3.5 Forces and the Magnetic Stress Tensor
127(2)
3.6 Magnetic Media
129(15)
3.6.1 Paramagnetic Materials
137(5)
3.6.2 Diamagnetic Materials
142(2)
3.7 B and H
144(2)
Exercises
146(11)
Chapter 4 Induction and Quasi-Stationary Phenomena 157(30)
1.1 Effect of Time Variations on x B and x H
157(3)
1.2 Induction Phenomena
160(2)
1.3 Temporal Variation of a Flux through a Moving Surface Element
162(3)
1.4 Differential Formulation of the Law of Induction
165(5)
1.5 Quasi-Stationary Phenomena
170(1)
1.6 Self-Inductance and Mutual Inductance
171(6)
1.7 About Units
177(2)
Exercises
179(8)
Chapter 5 General Discussion of Maxwell Equations 187(62)
5.1 Introduction
187(1)
5.2 Field Equations, Forces Acting on Charged Matter, and Conservation Laws
187(7)
5.3 Conservation Laws for the Macroscopic Case
194(4)
5.4 Energy and Momentum Conservation in General
198(1)
5.5 Complex Field
199(2)
5.6 Electromagnetic Waves in Vacuum and in Continuous Media
201(7)
5.7 Radiation Pressure
208(3)
5.8 Reflection of Waves
211(12)
5.9 Electromagnetic Waves in a Conducting Medium
223(7)
5.10 Electromagnetic Potentials and Gauge Transformations
230(11)
Exercises
241(8)
Chapter 6 Theory of Relativity: I 249(64)
6.1 Principle of Relativity in Mechanics and Electrodynamics
249(2)
6.1.1 Galileian Transformation
249(2)
6.2 The Search for an Absolute Frame Tied to the Ether
251(5)
6.3 Einstein's Postulates
256(1)
6.4 Lorentz Transformation
256(5)
6.5 Lorentz Contraction, Time Dilation, and Addition of Velocities
261(4)
6.6 Minkowski Notation
265(2)
6.7 General Lorentz Transformation
267(8)
6.8 Scalars, Vectors, and Tensors in Four Dimensions
275(7)
6.9 Four-Velocity, Four-Acceleration, and Proper Time
282(2)
6.10 Lorentz-Covariant Form of the Potential Equations
284(3)
6.11 Plane Waves
287(9)
6.12 The Twin Paradox
296(5)
Exercises
301(12)
Chapter 7 Theory of Relativity: II 313(54)
7.1 Lorentz Transformation and E and B Fields
313(12)
7.2 Charged Mass Point in Electromagnetic Field Minkowski Force
325(6)
7.3 Gauss's Theorem in Four Dimensions
331(6)
7.4 Electromagnetic Energy-Momentum Tensor
337(9)
7.5 Green's Functions for the Potential Equations
346(7)
7.6 Retarded. Advanced, and Symmetrical Potentials
353(4)
Exercises
357(10)
Chapter 8 Radiation from a Moving Point Charge 367(56)
8.1 Liénard-Wiechert Potentials of a Moving Point Charge
367(6)
8.2 Fields of a Moving Point Charge
373(15)
8.3 Fields of a Slow-Moving Point Charge
388(7)
8.3.1 General Case
388(2)
8.3.2 Small Periodic Oscillations in One Dimension
390(5)
8.4 Radiation from a Moving Charged Particle
395(13)
8.4.1 Parallel Velocity and Acceleration
399(6)
8.4.2 Perpendicular Velocity and Acceleration
405(3)
8.5 Synchrotron Radiation
408(8)
Exercises
416(7)
Chapter 9 Radiation Damping and Electromagnetic Mass 423(30)
9.1 Introduction
423(2)
9.2 Evaluation of the Self-Force and Radiation Damping
425(13)
9.3 Energy Loss by Radiation. Application to Periodic Motion
438(1)
9.4 Forced Vibrations
439(3)
9.5 Scattering of Radiation
442(8)
9.5.1 Rayleigh Scattering
445(1)
9.5.2 Thomson Scattering
446(1)
9.5.3 Resonance Scattering
447(3)
Exercises
450(3)
Chapter 10 Radiation from Periodic Charge and Current Distributions 453(30)
10.1 Multipole Expansion
453(12)
10.2 Electric and Magnetic Multipoles
465(3)
10.3 Multipole Expansion Using Spherical Harmonics
468(4)
10.4 Angular Distribution of Multipole Radiation
472(7)
Exercises
479(4)
Chapter 11 Lagrangian and Hamiltonian
Formulations of Electrodynamics
483(1)
11.1 Outline of Classical Mechanics
483(3)
11.2 Lagrangian Formulation of the Motion of a Charged Particle in Given Fields
486(2)
11.3 Hamiltonian Formulation of the Motion of a Charged Particle in Given Fields
488(4)
11.4 Lagrangian Formulation of the Maxwell Equations
492(12)
11.5 Hamiltonian Formulation of the Maxwell Equations
504(4)
11.6 Poisson Bracket Method
508(10)
11.7 Hamiltonian of a Closed System
518(7)
Exercises
525(2)
Chapter 12 Electromagnetic Properties of Matter 527(40)
12.1 Normal and Anomalous Dispersion
527(9)
12.2 Multiple Scattering Theory of the Index of Refraction
536(12)
12.3 Kramers-Kronig Relations
548(7)
12.4 General Observations on the Kramers-Kronig Relations
555(4)
12.5 Relaxation
559(3)
12.6 Plasma Frequency
562(2)
Exercises
564(3)
Appendix A. How to Convert a Given Amount of a Quantity from SI Units to Gaussian Units 567(2)
Appendix B. How to Convert an Equation from SI Units to Gaussian Units 569(2)
Bibliography 571(2)
Author Index 573(1)
Subject Index 574(5)
Solutions Manual 579
Preface
581(2)
Chapter 1
583(10)
Chapter 2
593(36)
Chapter 3
629(18)
Chapter 4
647(14)
Chapter 5
661(14)
Chapter 6
675(12)
Chapter 7
687(28)
Chapter 8
715(12)
Chapter 9
727(12)
Chapter 10
739(10)
Chapter 11
749(4)
Chapter 12
753

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