Maxwell's Equations

309 Pages·2009·47.045 MB·English

by  Paul G. Huray

Maxwell's
Equations

Maxwell's
Equations
Paul G. Huray
♦IEEE
IEEE PRESS
©WILEY
A John Wiley & Sons, Inc., Publication
Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or
otherwise, except as permitted under Section 107 or 108 of the 1976 United States
Copyright Act, without either the prior written permission of the Publisher, or authorization
through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc.,
222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the
web at www.copyright.com . Requests to the Publisher for permission should be addressed
to the Permissions Department, John Wiley & Sons, Inc., Ill River Street, Hoboken, NJ
07030, [phone], fax [phone], or online at http://www.wiley.com/go/
permission.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their
best efforts in preparing this book, they make no representations or warranties with respect
to the accuracy or completeness of the contents of this book and specifically disclaim any
implied warranties of merchantability or fitness for a particular purpose. No warranty may
be created or extended by sales representatives or written sales materials. The advice and
strategies contained herein may not be suitable for your situation. You should consult with
a professional where appropriate. Neither the publisher nor author shall be liable for any
loss of profit or any other commercial damages, including but not limited to special,
incidental, consequential, or other damages.
For general information on our other products and services or for technical support, please
contact our Customer Care Department within the United States at [phone], outside
the United States at [phone] or fax [phone].
Wiley also publishes its books in a variety of electronic formats. Some content that appears
in print may not be available in electronic formats. For more information about Wiley
products, visit our web site at www.wiley.com.
Library of Congress Cataloging-in-Pubtication Data:
Huray, Paul G., 1941-
Maxwell's equations / Paul G. Huray.
p. cm.
Includes bibliographical references.
ISBN 978-0-470-54276-7 (cloth)
1. Maxwell equations. I. Title.
QC670.H87 2010
530.l4'l-dc22
2009019340
Printed in the United States of America
10 9 8 7 6 5 4 3 21
This book is dedicated to the author's lifelong partner
Susan Lyons Huray

Contents
Acknowledgments
Introduction
1. Foundations of Maxwell's Equations
1.1 Historical Overview 1
1.2 Role of Electromagnetic Field Theory 2
1.3 Electromagnetic Field Quantities 3
1.4 Units and Universal Constants 6
1.5 Precision of Measured Quantities 12
1.6 Introduction to Complex Variables 12
1.7 Phasor Notation 15
1.8 Quaternions 19
1.9 Original Form of Maxwell's Equations 20
Endnotes 22
2. Vector Analysis 23
Introduction 23
2.1 Addition and Subtraction 23
2.2 Multiplication 26
2.3 Triple Products 29
2.4 Coordinate Systems 30
2.5 Coordinate Transformations 35
2.6 Vector Differentiation 39
2.7 Divergence Theorem 46
2.8 Stokes's Theorem 50
2.9 Laplacian of a Vector Field 51
Endnotes 55
3. Static Electric Fields 56
Introduction 56
3.1 Properties of Electrostatic Fields 56
3.2 Gauss's Law 58
3.3 Conservation Law 71
vii
viïi Contents
3.4 Electric Potential 72
3.5 Electric Field for a System of Charges 76
3.6 Electric Potential for a System of Charges 77
3.7 Electric Field for a Continuous Distribution 79
3.8 Conductor in a Static Electric Field 80
3.9 Capacitance 84
3.10 Dielectrics 87
3.11 Electric Flux Density 90
3.12 Dielectric Boundary Conditions 91
3.13 Electrostatic Energy 93
3.14 Electrostatic Field in a Dielectric 98
Endnotes 103
4. Solution of Electrostatic Problems 104
Introduction 104
4.1 Poisson's and Laplace's Equations 104
4.2 Solutions to Poisson's and Laplace's Equations 106
4.3 Green's Functions 110
4.4 Uniqueness of the Electrostatic Solution 114
4.5 Method of Images 116
5. Steady Electric Currents 129
Introduction 129
5.1 Current Density and Ohm's Law 129
5.2 Relation to Circuit Parameters 134
5.3 Superconductivity 136
5.4 Free Electron Gas Theory 139
5.5 Band Theory 145
5.6 Equation of Continuity 150
5.7 Microscopic View of Ohm's Law 151
5.8 Power Dissipation and Joule's Law 155
5.9 Boundary Condition for Current Density 155
5.10 Resistance/Capacitance Calculations 157
Endnote 158
6. Static Magnetic Fields 159
Introduction 159
6.1 Magnetic Force 160
6.2 Magnetostatics in Free Space 161
6.3 Magnetic Vector Potential 165
6.4 The Biot-Savart Law 167
6.5 Historical Conclusions 170
6.6 Atomic Magnetism 171
Contents ix
6.7 Magnetization 182
6.8 Equivalent Surface Current Density 184
6.9 Equivalent Magnetic Monopole Charge Density 184
6.10 Magnetic Field Intensity and Permeability 187
6.11 Ferromagnetism 188
6.12 Boundary Conditions for Magnetic Fields 193
6.13 Inductance and Inductors 194
6.14 Torque and Energy 198
Endnotes 202
7. Time-Varying Fields 203
Introduction 203
7.1 Faraday's Law of Induction 204
7.2 E&M Equations before Maxwell 205
7.3 Maxwell's Displacement Current 206
7.4 Integral Form of Maxwell's Equations 208
7.5 Magnetic Vector Potential 209
7.6 Solution of the Time-Dependent Inhomogeneous Potential
Wave Equations 213
7.7 Electric and Magnetic Field Equations for Source-Free Problems 214
7.8 Solutions for the Homogeneous Wave Equation 215
7.9 Particular Solution for the Inhomogeneous Wave Equation 221
7.10 Time-Harmonic Fields 227
7.11 Electromagnetic Spectrum 228
7.12 Electromagnetic Boundary Conditions 228
7.13 Particular Solution for the Wave Equation with Inhomogeneous
Boundary Conditions 236
7.14 Memristors 238
7.15 Electric Vector Potential 241
Endnotes 246
Appendix A: Measurement Errors 247
Appendix B: Graphics and Conformai Mapping 260
Appendix C: Vectors, Matrices, Orthogonal Functions 274
Bibliography 285
Index 287