© 2001 by CRC Press LLC Electrical Engineering Textbook Series Richard C. Dorf, Series Editor University of California, Davis Forthcoming Titles Applied Vector Analysis Matiur Rahman and Issac Mulolani Optimal Control Systems Subbaram Naidu Continuous Signals and Systems with MATLAB Taan ElAli and Mohammad A. Karim Discrete Signals and Systems with MATLAB Taan ElAli © 2001 by CRC Press LLC Edward J. Rothwell Michigan State University East Lansing, Michigan Michael J. Cloud Lawrence Technological University Southfield, Michigan Boca Raton London New York Washington, D.C. CRC Press This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. 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Visit our website at www.crcpress.com. © 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1397-X Library of Congress Card Number 00-065158 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Library of Congress Cataloging-in-Publication Data Rothwell, Edward J. Electromagnetics / Edward J. Rothwell, Michael J. Cloud. p. cm.—(Electrical engineering textbook series ; 2) Includes bibliographical references and index. ISBN 0-8493-1397-X (alk. paper) 1. Electromagnetic theory. I. Cloud, Michael J. II. Title. III. Series. QC670 .R693 2001 530.14 ′ 1—dc21 00-065158 CIP In memory of Catherine Rothwell © 2001 by CRC Press LLC Preface This book is intended as a text for a first-year graduate sequence in engineering electro- magnetics. Ideally such a sequence provides a transition period during which a student can solidify his or her understanding of fundamental concepts before proceeding to spe- cialized areas of research. The assumed background of the reader is limited to standard undergraduate topics in physics and mathematics. Worthy of explicit mention are complex arithmetic, vec- tor analysis, ordinary differential equations, and certain topics normally covered in a “signals and systems” course (e.g., convolution and the Fourier transform). Further an- alytical tools, such as contour integration, dyadic analysis, and separation of variables, are covered in a self-contained mathematical appendix. The organization of the book is in six chapters. In Chapter 1 we present essential background on the field concept, as well as information related specifically to the electro- magnetic field and its sources. Chapter 2 is concerned with a presentation of Maxwell’s theory of electromagnetism. Here attention is given to several useful forms of Maxwell’s equations, the nature of the four field quantities and of the postulate in general, some fundamental theorems, and the wave nature of the time-varying field. The electrostatic and magnetostatic cases are treated in Chapter 3. In Chapter 4 we cover the representa- tion of the field in the frequency domains: both temporal and spatial. Here the behavior of common engineering materials is also given some attention. The use of potential functions is discussed in Chapter 5, along with other field decompositions including the solenoidal–lamellar, transverse–longitudinal, and TE–TM types. Finally, in Chapter 6 we present the powerful integral solution to Maxwell’s equations by the method of Strat- ton and Chu. A main mathematical appendix near the end of the book contains brief but sufficient treatments of Fourier analysis, vector transport theorems, complex-plane inte- gration, dyadic analysis, and boundary value problems. Several subsidiary appendices provide useful tables of identities, transforms, and so on. We would like to express our deep gratitude to those persons who contributed to the development of the book. The reciprocity-based derivation of the Stratton–Chu formula was provided by Prof. Dennis Nyquist, as was the material on wave reflection from multiple layers. The groundwork for our discussion of the Kronig–Kramers relations was provided by Michael Havrilla, and material on the time-domain reflection coefficient was developed by Jungwook Suk. We owe thanks to Prof. Leo Kempel, Dr. David Infante, and Dr. Ahmet Kizilay for carefully reading large portions of the manuscript during its preparation, and to Christopher Coleman for helping to prepare the figures. We are indebted to Dr. John E. Ross for kindly permitting us to employ one of his computer programs for scattering from a sphere and another for numerical Fourier transformation. Helpful comments and suggestions on the figures were provided by Beth Lannon–Cloud. © 2001 by CRC Press LLC Thanks to Dr. C. L. Tondo of T & T Techworks, Inc., for assistance with the LaTeX macros that were responsible for the layout of the book. Finally, we would like to thank the staff members of CRC Press — Evelyn Meany, Sara Seltzer, Elena Meyers, Helena Redshaw, Jonathan Pennell, Joette Lynch, and Nora Konopka — for their guidance and support. © 2001 by CRC Press LLC Contents Preface 1Introductoryconcepts 1.1Notation,conventions,andsymbology 1.2Thefieldconceptofelectromagnetics 1.2.1Historicalperspective 1.2.2Formalizationoffieldtheory 1.3Thesourcesoftheelectromagneticfield 1.3.1Macroscopicelectromagnetics 1.3.2Impressedvs.secondarysources 1.3.3Surfaceandlinesourcedensities 1.3.4Chargeconservation 1.3.5Magneticcharge 1.4Problems 2Maxwell’stheoryofelectromagnetism 2.1Thepostulate 2.1.1TheMaxwell–Minkowskiequations 2.1.2Connectiontomechanics 2.2Thewell-posednatureofthepostulate 2.2.1UniquenessofsolutionstoMaxwell’sequations 2.2.2Constitutiverelations 2.3Maxwell’sequationsinmovingframes 2.3.1FieldconversionsunderGalileantransformation 2.3.2FieldconversionsunderLorentztransformation 2.4TheMaxwell–Boffiequations 2.5Large-scaleformofMaxwell’sequations 2.5.1Surfacemovingwithconstantvelocity 2.5.2Moving,deformingsurfaces 2.5.3Large-scaleformoftheBoffiequations 2.6Thenatureofthefourfieldquantities 2.7Maxwell’sequationswithmagneticsources 2.8Boundary(jump)conditions 2.8.1Boundaryconditionsacrossastationary,thinsourcelayer 2.8.2Boundaryconditionsacrossastationarylayeroffielddiscontinuity 2.8.3Boundaryconditionsatthesurfaceofaperfectconductor © 2001 by CRC Press LLC 2.8.4Boundaryconditionsacrossastationarylayeroffielddiscontinuityusing equivalentsources 2.8.5Boundaryconditionsacrossamovinglayeroffielddiscontinuity 2.9Fundamentaltheorems 2.9.1Linearity 2.9.2Duality 2.9.3Reciprocity 2.9.4Similitude 2.9.5Conservationtheorems 2.10Thewavenatureoftheelectromagneticfield 2.10.1Electromagneticwaves 2.10.2Waveequationforbianisotropicmaterials 2.10.3Waveequationinaconductingmedium 2.10.4Scalarwaveequationforaconductingmedium 2.10.5FieldsdeterminedbyMaxwell’sequationsvs.fieldsdeterminedbythe waveequation 2.10.6Transientuniformplanewavesinaconductingmedium 2.10.7Propagationofcylindricalwavesinalosslessmedium 2.10.8Propagationofsphericalwavesinalosslessmedium 2.10.9Nonradiatingsources 2.11Problems 3Thestaticelectromagneticfield 3.1Staticfieldsandsteadycurrents 3.1.1Decouplingoftheelectricandmagneticfields 3.1.2Staticfieldequilibriumandconductors 3.1.3Steadycurrent 3.2Electrostatics 3.2.1Theelectrostaticpotentialandwork 3.2.2Boundaryconditions 3.2.3Uniquenessoftheelectrostaticfield 3.2.4Poisson’sandLaplace’sequations 3.2.5Forceandenergy 3.2.6Multipoleexpansion 3.2.7Fieldproducedbyapermanentlypolarizedbody 3.2.8Potentialofadipolelayer 3.2.9Behaviorofelectricchargedensitynearaconductingedge 3.2.10SolutiontoLaplace’sequationforbodiesimmersedinanimpressedfield 3.3Magnetostatics 3.3.1Themagneticvectorpotential 3.3.2Multipoleexpansion 3.3.3Boundaryconditionsforthemagnetostaticfield 3.3.4Uniquenessofthemagnetostaticfield 3.3.5Integralsolutionforthevectorpotential 3.3.6Forceandenergy 3.3.7Magneticfieldofapermanentlymagnetizedbody 3.3.8Bodiesimmersedinanimpressedmagneticfield:magnetostaticshielding 3.4Staticfieldtheorems © 2001 by CRC Press LLC 3.4.1Meanvaluetheoremofelectrostatics 3.4.2Earnshaw’stheorem 3.4.3Thomson’stheorem 3.4.4Green’sreciprocationtheorem 3.5Problems 4Temporalandspatialfrequencydomainrepresentation 4.1Interpretationofthetemporaltransform 4.2Thefrequency-domainMaxwellequations 4.3Boundaryconditionsonthefrequency-domainfields 4.4TheconstitutiveandKronig–Kramersrelations 4.4.1Thecomplexpermittivity 4.4.2Highandlowfrequencybehaviorofconstitutiveparameters 4.4.3TheKronig–Kramersrelations 4.5Dissipatedandstoredenergyinadispersivemedium 4.5.1Dissipationinadispersivematerial 4.5.2Energystoredinadispersivematerial 4.5.3Theenergytheorem 4.6Somesimplemodelsforconstitutiveparameters 4.6.1Complexpermittivityofanon-magnetizedplasma 4.6.2Complexdyadicpermittivityofamagnetizedplasma 4.6.3Simplemodelsofdielectrics 4.6.4Permittivityandconductivityofaconductor 4.6.5Permeabilitydyadicofaferrite 4.7Monochromaticfieldsandthephasordomain 4.7.1Thetime-harmonicEMfieldsandconstitutiverelations 4.7.2ThephasorfieldsandMaxwell’sequations 4.7.3Boundaryconditionsonthephasorfields 4.8Poynting’stheoremfortime-harmonicfields 4.8.1GeneralformofPoynting’stheorem 4.8.2Poynting’stheoremfornondispersivematerials 4.8.3Lossless,lossy,andactivemedia 4.9ThecomplexPoyntingtheorem 4.9.1Boundaryconditionforthetime-averagePoyntingvector 4.10Fundamentaltheoremsfortime-harmonicfields 4.10.1Uniqueness 4.10.2Reciprocityrevisited 4.10.3Duality 4.11Thewavenatureofthetime-harmonicEMfield 4.11.1Thefrequency-domainwaveequation 4.11.2Fieldrelationshipsandthewaveequationfortwo-dimensionalfields 4.11.3Planewavesinahomogeneous,isotropic,lossymaterial 4.11.4Monochromaticplanewavesinalossymedium 4.11.5Planewavesinlayeredmedia 4.11.6Plane-wavepropagationinananisotropicferritemedium 4.11.7Propagationofcylindricalwaves 4.11.8Propagationofsphericalwavesinaconductingmedium 4.11.9Nonradiatingsources © 2001 by CRC Press LLC [...]... operator notation ∇ for gradient, curl, divergence, Laplacian, and so on The SI (MKS) system of units is employed throughout the book © 2001 by CRC Press LLC 1.2 The field concept of electromagnetics Introductory treatments of electromagnetics often stress the role of the field in force transmission: the individual fields E and B are defined via the mechanical force on a small test charge This is certainly... that given by its mathematical implications? In this book, E, D, B, and H are integral parts of a field-theory description of electromagnetics In any field theory we need two types of fields: a mediating field generated by a source, and a field describing the source itself In free-space electromagnetics the mediating field consists of E and B, while the source field is the distribution of charge or current An... the properties of the electromagnetic field with a detailed examination of its source 1.3.1 Macroscopic electromagnetics We are interested primarily in those electromagnetic effects that can be predicted by classical techniques using continuous sources (charge and current densities) Although macroscopic electromagnetics is limited in scope, it is useful in many situations encountered by engineers These... viable alternative is to use atomic theories of matter to estimate the useful scope of macroscopic electromagnetics Remember, we are completely free to postulate a theory of nature whose scope may be limited Like continuum mechanics, which treats distributions of matter as if they were continuous, macroscopic electromagnetics is regarded as valid because it is verified by experiment over a certain range... action-at-a-distance interpretations of physical laws such as Newton’s law of gravitation or the interaction of charged particles If Coulomb’s law were taken as the force law in a mechanical description of electromagnetics, the state of a system of particles could be described completely in terms of their positions, momenta, and charges Of course, charged particle interaction is not this simple An attempt... by antennas Macroscopic predictions can fall short in cases where quantum effects are important: e.g., with devices such as tunnel diodes Even so, quantum mechanics can often be coupled with classical electromagnetics to determine the macroscopic electromagnetic properties of important materials Electric charge is not of a continuous nature The quantization of atomic charge — ±e for electrons and protons,... the static potential field theory to the realm of mechanics via the electrostatic force F = qE acting on a particle of charge q In future chapters we shall present a classical field theory for macroscopic electromagnetics In that case the mediating field quantities are E, D, B, and H, and the source field is the current density J 1.3 The sources of the electromagnetic field Electric charge is an intriguing... range generally corresponds to dimensions on a laboratory scale, implying a very wide range of validity for engineers © 2001 by CRC Press LLC Macroscopic effects as averaged microscopic effects Macroscopic electromagnetics can hold in a world of discrete charges because applications usually occur over physical scales that include vast numbers of charges Common devices, generally much larger than individual... do we consider the dipole nature of polarizable materials or the microscopic motion associated with molecular magnetic moment or the magnetic moment of free charge For the consideration of free-space electromagnetics, we assume charge exhibits either three degrees of freedom (volume charge), two degrees of freedom (surface charge), or one degree of freedom (line charge) In typical matter, the microscopic... voltage excitations that are independent of applied load In this way they differ from the secondary or “dependent” sources that react to the effect produced by the application of primary sources In applied electromagnetics the primary source may be so distant that return effects resulting from local interaction of its impressed fields can be ignored Other examples of primary sources include the applied voltage . LLC Contents Preface 1Introductoryconcepts 1.1Notation,conventions,andsymbology 1.2Thefieldconceptofelectromagnetics 1.2.1Historicalperspective 1.2.2Formalizationoffieldtheory 1.3Thesourcesoftheelectromagneticfield 1.3.1Macroscopicelectromagnetics 1.3.2Impressedvs.secondarysources 1.3.3Surfaceandlinesourcedensities 1.3.4Chargeconservation 1.3.5Magneticcharge 1.4Problems 2Maxwell’stheoryofelectromagnetism 2.1Thepostulate 2.1.1TheMaxwell–Minkowskiequations 2.1.2Connectiontomechanics 2.2Thewell-posednatureofthepostulate 2.2.1UniquenessofsolutionstoMaxwell’sequations 2.2.2Constitutiverelations 2.3Maxwell’sequationsinmovingframes 2.3.1FieldconversionsunderGalileantransformation 2.3.2FieldconversionsunderLorentztransformation 2.4TheMaxwell–Boffiequations 2.5Large-scaleformofMaxwell’sequations 2.5.1Surfacemovingwithconstantvelocity 2.5.2Moving,deformingsurfaces 2.5.3Large-scaleformoftheBoffiequations 2.6Thenatureofthefourfieldquantities 2.7Maxwell’sequationswithmagneticsources 2.8Boundary(jump)conditions 2.8.1Boundaryconditionsacrossastationary,thinsourcelayer 2.8.2Boundaryconditionsacrossastationarylayeroffielddiscontinuity 2.8.3Boundaryconditionsatthesurfaceofaperfectconductor ©. book. © 2001 by CRC Press LLC 1.2 The field concept of electromagnetics Introductory treatments of electromagnetics often stress the role of the field in