Classical Theory of Electromagnetism

by Bartolo, Baldassare Di

• ISBN13: 9789812382191
• ISBN10: 9812382194
• Edition: 2nd
• Format: Paperback
• Copyright: 2004-11-01
• Publisher: World Scientific Pub Co Inc

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, Pι (cos theta)	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 Dirichlet 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)
4.1 Effect of Time Variations on x B and x H	157	(3)
4.2 Induction Phenomena	160	(2)
4.3 Temporal Variation of a Flux through a Moving Surface Element	162	(3)
4.4 Differential Formulation of the Law of Induction	165	(5)
4.5 Quasi-Stationary Phenomena	170	(1)
4.6 Self-Inductance and Mutual Inductance	171	(6)
4.7 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 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	(44)
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