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
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.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, microfilming, and recording, or by any information storage or
retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for
creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC
for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431, or visit
our Web site at www.crcpress.com
Trademark Notice:
Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation, without intent to infringe.
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
Preface
Thisbookisintendedasatextfora?rst-yeargraduatesequenceinengineeringelectro-
magnetics.Ideallysuchasequenceprovidesatransitionperiodduringwhichastudent
cansolidifyhisorherunderstandingoffundamentalconceptsbeforeproceedingtospe-
cializedareasofresearch.
Theassumedbackgroundofthereaderislimitedtostandardundergraduatetopics
inphysicsandmathematics. Worthyofexplicitmentionarecomplexarithmetic,vec-
toranalysis,ordinarydi?erentialequations,andcertaintopicsnormallycoveredina
“signalsandsystems”course(e.g.,convolutionandtheFouriertransform).Furtheran-
alyticaltools,suchascontourintegration,dyadicanalysis,andseparationofvariables,
arecoveredinaself-containedmathematicalappendix.
Theorganizationofthebookisinsixchapters. InChapter1wepresentessential
backgroundonthe?eldconcept,aswellasinformationrelatedspeci?callytotheelectro-
magnetic?eldanditssources.Chapter2isconcernedwithapresentationofMaxwell’s
theoryofelectromagnetism.HereattentionisgiventoseveralusefulformsofMaxwell’s
equations,thenatureofthefour?eldquantitiesandofthepostulateingeneral,some
fundamentaltheorems,andthewavenatureofthetime-varying?eld.Theelectrostatic
andmagnetostaticcasesaretreatedinChapter3.InChapter4wecovertherepresenta-
tionofthe?eldinthefrequencydomains:bothtemporalandspatial.Herethebehavior
ofcommonengineeringmaterialsisalsogivensomeattention. Theuseofpotential
functionsisdiscussedinChapter5,alongwithother?elddecompositionsincludingthe
solenoidal–lamellar,transverse–longitudinal,andTE–TMtypes. Finally,inChapter6
wepresentthepowerfulintegralsolutiontoMaxwell’sequationsbythemethodofStrat-
tonandChu.Amainmathematicalappendixneartheendofthebookcontainsbriefbut
su?cienttreatmentsofFourieranalysis,vectortransporttheorems,complex-planeinte-
gration,dyadicanalysis,andboundaryvalueproblems. Severalsubsidiaryappendices
provideusefultablesofidentities,transforms,andsoon.
Wewouldliketoexpressourdeepgratitudetothosepersonswhocontributedtothe
developmentofthebook.Thereciprocity-basedderivationoftheStratton–Chuformula
wasprovidedbyProf.DennisNyquist, aswasthematerialonwave re?ectionfrom
multiplelayers.ThegroundworkforourdiscussionoftheKronig–Kramersrelationswas
providedbyMichaelHavrilla,andmaterialonthetime-domainre?ectioncoe?cientwas
developedbyJungwookSuk. WeowethankstoProf.LeoKempel,Dr.DavidInfante,
andDr.AhmetKizilayforcarefullyreadinglargeportionsofthemanuscriptduringits
preparation,andtoChristopherColemanforhelpingtopreparethe?gures. Weare
indebtedtoDr.JohnE.Rossforkindlypermittingustoemployoneofhiscomputer
programsforscatteringfromasphereandanotherfornumericalFouriertransformation.
Helpfulcommentsandsuggestionsonthe?gureswereprovidedbyBethLannon–Cloud.
ThankstoDr.C.L.TondoofT&TTechworks,Inc.,forassistancewiththeLaTeX
macrosthatwereresponsibleforthelayoutofthebook.Finally,wewouldliketothank
thesta?membersofCRCPress—EvelynMeany,SaraSeltzer,ElenaMeyers,Helena
Redshaw,JonathanPennell,JoetteLynch,andNoraKonopka—fortheirguidanceand
support.
Contents
Preface
1Introductoryconcepts
1.1Notation,conventions,andsymbology
1.2The?eldconceptofelectromagnetics
1.2.1Historicalperspective
1.2.2Formalizationof?eldtheory
1.3Thesourcesoftheelectromagnetic?eld
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–Bo?equations
2.5Large-scaleformofMaxwell’sequations
2.5.1Surfacemovingwithconstantvelocity
2.5.2Moving,deformingsurfaces
2.5.3Large-scaleformoftheBo?equations
2.6Thenatureofthefour?eldquantities
2.7Maxwell’sequationswithmagneticsources
2.8Boundary(jump)conditions
2.8.1Boundaryconditionsacrossastationary,thinsourcelayer
2.8.2Boundaryconditionsacrossastationarylayerof?elddiscontinuity
2.8.3Boundaryconditionsatthesurfaceofaperfectconductor
2.8.4Boundaryconditionsacrossastationarylayerof?elddiscontinuityusing
equivalentsources
2.8.5Boundaryconditionsacrossamovinglayerof?elddiscontinuity
2.9Fundamentaltheorems
2.9.1Linearity
2.9.2Duality
2.9.3Reciprocity
2.9.4Similitude
2.9.5Conservationtheorems
2.10Thewavenatureoftheelectromagnetic?eld
2.10.1Electromagneticwaves
2.10.2Waveequationforbianisotropicmaterials
2.10.3Waveequationinaconductingmedium
2.10.4Scalarwaveequationforaconductingmedium
2.10.5FieldsdeterminedbyMaxwell’sequationsvs.?eldsdeterminedbythe
waveequation
2.10.6Transientuniformplanewavesinaconductingmedium
2.10.7Propagationofcylindricalwavesinalosslessmedium
2.10.8Propagationofsphericalwavesinalosslessmedium
2.10.9Nonradiatingsources
2.11Problems
3Thestaticelectromagnetic?eld
3.1Static?eldsandsteadycurrents
3.1.1Decouplingoftheelectricandmagnetic?elds
3.1.2Static?eldequilibriumandconductors
3.1.3Steadycurrent
3.2Electrostatics
3.2.1Theelectrostaticpotentialandwork
3.2.2Boundaryconditions
3.2.3Uniquenessoftheelectrostatic?eld
3.2.4Poisson’sandLaplace’sequations
3.2.5Forceandenergy
3.2.6Multipoleexpansion
3.2.7Fieldproducedbyapermanentlypolarizedbody
3.2.8Potentialofadipolelayer
3.2.9Behaviorofelectricchargedensitynearaconductingedge
3.2.10SolutiontoLaplace’sequationforbodiesimmersedinanimpressed?eld
3.3Magnetostatics
3.3.1Themagneticvectorpotential
3.3.2Multipoleexpansion
3.3.3Boundaryconditionsforthemagnetostatic?eld
3.3.4Uniquenessofthemagnetostatic?eld
3.3.5Integralsolutionforthevectorpotential
3.3.6Forceandenergy
3.3.7Magnetic?eldofapermanentlymagnetizedbody
3.3.8Bodiesimmersedinanimpressedmagnetic?eld:magnetostaticshielding
3.4Static?eldtheorems
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-domain?elds
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
4.7Monochromatic?eldsandthephasordomain
4.7.1Thetime-harmonicEM?eldsandconstitutiverelations
4.7.2Thephasor?eldsandMaxwell’sequations
4.7.3Boundaryconditionsonthephasor?elds
4.8Poynting’stheoremfortime-harmonic?elds
4.8.1GeneralformofPoynting’stheorem
4.8.2Poynting’stheoremfornondispersivematerials
4.8.3Lossless,lossy,andactivemedia
4.9ThecomplexPoyntingtheorem
4.9.1Boundaryconditionforthetime-averagePoyntingvector
4.10Fundamentaltheoremsfortime-harmonic?elds
4.10.1Uniqueness
4.10.2Reciprocityrevisited
4.10.3Duality
4.11Thewavenatureofthetime-harmonicEM?eld
4.11.1Thefrequency-domainwaveequation
4.11.2Fieldrelationshipsandthewaveequationfortwo-dimensional?elds
4.11.3Planewavesinahomogeneous,isotropic,lossymaterial
4.11.4Monochromaticplanewavesinalossymedium
4.11.5Planewavesinlayeredmedia
4.11.6Plane-wavepropagationinananisotropicferritemedium
4.11.7Propagationofcylindricalwaves
4.11.8Propagationofsphericalwavesinaconductingmedium
4.11.9Nonradiatingsources
4.12Interpretationofthespatialtransform
4.13SpatialFourierdecomposition
4.13.1BoundaryvalueproblemsusingthespatialFourierrepresentation
4.14Periodic?eldsandFloquet’stheorem
4.14.1Floquet’stheorem
4.14.2Examplesofperiodicsystems
4.15Problems
5FielddecompositionsandtheEMpotentials
5.1Spatialsymmetrydecompositions
5.1.1Planar?eldsymmetry
5.2Solenoidal–lamellardecomposition
5.2.1Solutionforpotentialsinanunboundedmedium:theretardedpotentials
5.2.2Solutionforpotentialfunctionsinaboundedmedium
5.3Transverse–longitudinaldecomposition
5.3.1Transverse–longitudinaldecompositionintermsof?elds
5.4TE–TMdecomposition
5.4.1TE–TMdecompositionintermsof?elds
5.4.2TE–TMdecompositionintermsofHertzianpotentials
5.4.3Application:hollow-pipewaveguides
5.4.4TE–TMdecompositioninsphericalcoordinates
5.5Problems
6IntegralsolutionsofMaxwell’sequations
6.1VectorKircho?solution
6.1.1TheStratton–Chufor mu la
6.1.2TheSommerfeldradiationcondition
6.1.3Fieldsintheexcludedregion:theextinctiontheorem
6.2Fieldsinanunboundedmedium
6.2.1Thefar-zone?eldsproducedbysourcesinunboundedspace
6.3Fieldsinabounded,source-freeregion
6.3.1ThevectorHuygensprinciple
6.3.2TheFranzformula
6.3.3Love’sequivalenceprinciple
6.3.4TheSchelkuno?equivalenceprinciple
6.3.5Far-zone?eldsproducedbyequivalentsources
6.4Problems
AMathematicalappendix
A.1TheFouriertransform
A.2Vectortransporttheorems
A.3Dyadicanalysis
A.4Boundaryvalueproblems
BUsefulidentities
CSomeFouriertransformpairs
DCoordinatesystems
EPropertiesofspecialfunctions
E.1Besselfunctions
E.2Legendrefunctions
E.3Sphericalharmonics
References
