Basic Electromagnetism PHYSICS and ITS APPLICATIONS Series Editors E.R

Basic Electromagnetism PHYSICS AND ITS APPLICATIONS Series Editors E.R. Dobbs S.B. Palmer University of London Warwick University This series of short texts on advanced topics for students, scientists and engineers will appeal to readers seeking to broaden their knowledge of the physics underlying modern technology. Each text provides a concise review of the fundamental physics and current developments in the area, with references to treatises and the primary literature to facilitate further study, Additionally texts providing a core course in physics are included to form a ready reference collection. The rapid pace of technological change today is based on the most recent scientific advances. This series is, therefore, particularly suitable for those engaged in research and development, who frequently require a rapid summary of another topic in physics or a new application of physical principles in their work. Many of the texts will also be suitable for final year undergraduate and postgraduate courses. 1. Electrons in Metals and Semiconductors R.G. Chambers 2. Basic Digital Electronics l.A. Strong 3. AC and DC Network Theory Anthony l. Painton and Harry M. Howarth 4. Nuclear and Particle Physics R.J. Blin-Stoyle 5. Thermal Physics Second edition C.B.P. Finn 6. Vacuum Physics and Techniques T.A. Delchar 7. Basic Electromagnetism E.R. Dobbs Basic Electromagnetism E. R. Dobbs Emeritus Professor of Physics Universityof London Springer-Science+Business Media, B.V. First edition 1993 © 1993 E.R. Dobbs Originally published by Chapman and HalI in 1993 Typeset in 10/12 Times by Thomson Press (India) Ltd, New Delhi ISBN 978-0-412-55570-1 ISBN 978-94-011-2112-5 (eBook) DOI 10.1007/978-94-011-2112-5 Apart from any fair dealing for the purposes or research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, Of transmitted, in any form or by any means, without the prior permission in writing of tl1$: publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. A Catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication data Dobbs, Roland, 1924- Basic electromagnetism / E. R. Dobbs.-lst ed. p. cm. -(Physics and its applications ; 7) Inc1udes index. 1. Electromagnetism. 1. Title. II. Series. QC760.D62 1993 93-7067 537-dc20 CIP I§ Printed on permanent acid-free text paper, manufactured in accordance with the proposed ANSIjNISO Z 39.48-199X and ANSI Z 39.48-1984 Contents Preface ix List of symbols xiii 1 Introduction 1 2 Electrostatics 4 2.1 Coulomb's law 4 2.2 Gauss's law 8 2.3 Electric potential 14 2.4 Electrostatic energy 19 2.5 Dielectrics 22 3 Electric potential and fields 30 3.1 Poisson's and Laplace's equations 30 3.2 Solutions of Laplace's equation 33 3.3 Electrical images 36 3.4 Electron optics 41 4 Magnetostatics 47 4.1 Electric current 47 4.2 Lorentz force 51 4.3 Biot-Savart law 57 4.4 Forces between currents 60 4.5 Ampere's law and magnetic flux 61 5 Electromagnetism 66 5.1 Faraday's law 66 5.2 Applications of Faraday's law 72 vi Contents 6 Magnetism 79 6.1 Magnetization of matter 79 6.2 Characteristics of Band H 84 6.3 Magnetism in matter 87 6.4 Production of magnetic fields 96 7 Maxwell's equations 102 7.1 Gauss's and Faraday's laws 102 7.2 Ampere's and Maxwell's laws 103 7.3 Statics and dynamics 105 7.4 Free space and matter 106 8 Electromagnetism and relativity 113 8.1 Lorentz transformations 113 8.2 Fields of moving charges 116 8.3 Vector potentials 123 8.4 Energy of electromagnetic field 129 8.5 Retarded potentials 132 9 Electromagnetic waves in space 135 9.1 Wave equations 135 9.2 Plane waves 137 9.3 Spherical waves 141 9.4 Energy density and energy flow 143 10 Electromagnetic waves in dielectrics 147 10.1 Polarization of dielectrics 147 10.2 Wave parameters in dielectrics 151 10.3 Absorption and dispersion 154 11 Reflection and refraction 160 11.1 Boundary relations 160 11.2 Fresnel's equations 164 11.3 Energy flow at a boundary 168 11.4 Total internal reflection 171 12 Electromagnetic waves in conductors 173 12.1 Wave parameters in conductors 174 12.2 Wave impedance and reflectance 177 12.3 Energy flow and radiation pressure 178 12.4 Plasmas 180 13 Generation of electromagnetic waves 183 13.1 Hertzian dipole 183 13.2 Radiant energy and power 187 Contents vii 13.3 Antennas 189 13.4 Scattering 193 14 Guided waves 196 14.1 Waveguide equation 196 14.2 Rectangular waveguides 198 14.3 Waveguide modes 202 14.4 Cavities 205 Further reading 210 Appendix A Electromagnetic quantities 211 Appendix B Gaussian units 214 Appendix C Physical constants 216 Appendix D Electromagnetic spectrum 217 Appendix E Vector calculus 218 Appendix F Lorentz transformations 221 Appendix G Exercises 223 Appendix H Answers to exercises 236 Index 239 Preface Electricity and magnetism are basic to our understanding of the properties of matter and yet are often regarded as the difficult parts of an undergraduate course in physics, materials science or engin eering. In the first six chapters of this book answers are developed from first principles to such questions as: What is electricity? What is electromagnetism? Why are some materials magnetic and others non-magnetic? What is magnetism? These questions can be answered in two related ways. On the one hand the classical explanation is in terms of classical concepts: electric charge (q), electric and magnetic fields (E and B) and electric currents. On the other hand the microscopic (or 'atomic') explanation is in terms of quantum concepts: electrons, nuclei, electron orbits in atoms, electron spin and photons. Microscopic explanations underlie classical ones, but they do not deny them. The great triumphs of classical theory are mechanics, gravitation, thermodynamics, electro magnetism and relativity. Historically the classical theories began at the time of Newton (seventeenth century) and were completed by Maxwell (nineteenth century) and by Einstein (early twentieth century). Microscopic explanations began with 1.1. Thomson's discovery of the electron in 1897. For most physical phenomena it is best to seek a classical explanation first, especially for phenomena at room temperature, or low energy, when quantum effects are small. This book presents classical theory in a logical, self-consistent sequence, but reference is made to microscopic (quantum) theory at each appropriate stage. Electromagnetism began in 1819 with the discovery by Oersted that an electric current is associated with a magnetic field and was followed in 1820 by Ampere's discovery that two wires carrying x Preface electric currents exerted magnetic forces on one another. But it was Faraday's discovery of electromagnetic induction in 1831, or as he put it, the conversion of magnetism into electricity, that finally showed that electricity and magnetism were not distinct, separate phenomena, but interacted when there were time-varying electric or magnetic fields. The beauty of electromagnetism is that Faraday's experiments led to a symmary of the whole of electromagnetism in just the four equations of Maxwell's theory, which relate E and B in space with fixed and moving charges, together with the electromagnetic force law. These equations are greatly simplified when we deal with statics, that is, variables that do not depend on time t, or stationary variables. Maxwell's equations then simplify and separate into two independent pairs of equations: 1. The first pair describe the electrostatic field E for fixed charges and are known as Gauss's law and the circulation law. They summarize electrostatics. 2. The second pair describe the magnetostatic field B for steady currents (charges moving at constant speed) and are known as Gauss's law and Ampere's law. They summarize magnetostatics. In electrostatics only the E field appears and iJE/iJt = 0; in magneto statics only the Bfield appears and fJB/fJt = O. So under these conditions, electricity and magnetism are classically distinct, separate phenomena. But if you charge a capacitor (q varying with time) or move a magnet (B at a point varying in time) then E and B are no longer independent and new terms in the equations due to electromagnetism appear, as first discovered by Faraday (Faraday's law) and Maxwell (Maxwell's law). The development of the subject in this text is therefore first electro statics, then magnetostatics, followed by electromagnetism and magnetism. The seventh chapter summarizes electromagnetism in terms of Maxwell's equations, which are then used to study the propagation and generation of electromagnetic waves. The first seven chapters often comprise a first course in electromagnetism for undergraduates. In studying the solutions of Maxwell's equations you will find answers to such questions as: What is an electromagnetic wave? Why does a radio wave travel through space at the speed of light? How is a radio wave generated? Why does light pass through a straight tunnel when a radio wave does not? How does· light travel down a curved glass fibre? Preface xi Before studying these solutions, Chapter 8 discusses the remarkable fact that the classical laws of electromagnetism are fully consistent with Einstein's special theory of relativity.

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