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Electromagnetic Fields Second Edition Jean G.Van Bladel IEEE Antennas and Propagation Society, Sponsor IEEE Press Series on ElectromagneticWaveTheory DonaldG.Dudley,SeriesEditor IEEEPRESS “ffirs” — 2007/5/4 — page iii — #3 “ffirs” — 2007/5/4 — page vi — #6 Electromagnetic Fields “ffirs” — 2007/5/4 — page i — #1 IEEEPRESSSERIESONELECTROMAGNETICWAVETHEORY The IEEE Press Series on ElectromagneticWaveTheory consists of new titles as well as reissues and revisionsofrecognizedclassicsinelectromagneticwavesandapplicationswhichmaintainlong-termarchival significance. SeriesEditor DonaldG.Dudley UniversityofArizona AdvisoryBoard RobertE.Collin CaseWesternReserveUniversity AkiraIshimaru DouglasS.Jones UniversityofWashington UniversityofDundee AssociateEditors ELECTROMAGNETICTHEORY,SCATTERING, INTEGRALEQUATIONMETHODS ANDDIFFRACTION DonaldR.Wilton EhudHeyman UniversityofHouston TelAvivUniversity DIFFERENTIALEQUATIONMETHODS ANTENNAS,PROPAGATION,ANDMICROWAVES AndreasC.Cangellaris DavidR.Jackson UniversityofIllinoisatUrbana-Champaign UniversityofHouston BOOKSINTHEIEEEPRESSSERIESONELECTROMAGNETICWAVETHEORY Chew,W.C.,WavesandFieldsinInhomogeneousMedia Christopoulos,C.,TheTransmission-LineModelingMethods:TLM Clemmow,P.C.,ThePlaneWaveSpectrumRepresentationofElectromagneticFields Collin,R.E.,FieldTheoryforGuidedWaves,SecondEdition Collin,R.E.,FoundationsforMicrowaveEngineering,SecondEdition Dudley,D.G.,MathematicalFoundationsforElectromagneticTheory Elliott,R.S.,AntennaTheoryandDesign,RevisedEdition Elliott,R.S.,Electromagnetics:History,Theory,andApplications Felsen,L.B.,andMarcuvitz,N.,RadiationandScatteringofWaves Harrington,R.F.,FieldComputationbyMomentMethods Harrington,R.F.,TimeHarmonicElectromagneticFields Hansen,T.B.,andYaghjian,A.D.,Plane-WaveTheoryofTime-DomainFields Ishimaru,A.,WavePropagationandScatteringinRandomMedia Jones,D.S.,MethodsinElectromagneticWavePropagation,SecondEdition Josefsson,L.,andPersson,P.,ConformalArrayAntennaTheoryandDesign Lindell,I.V.,MethodsforElectromagneticFieldAnalysis Lindell,I.V.,DifferentialFormsinElectromagnetics Stratton,J.A.,ElectromagneticTheory,AClassicReissue Tai,C.T.,GeneralizedVectorandDyadicAnalysis,SecondEdition VanBladel,J.G.,ElectromagneticFields,SecondEdition VanBladel,J.G.,SingularElectromagneticFieldsandSources Volakis,etal.,FiniteElementMethodforElectromagnetics Zhu,Y.,andCangellaris,A.,MultigridFiniteElementMethodsforElectromagneticFieldModeling “ffirs” — 2007/5/4 — page ii — #2 Electromagnetic Fields Second Edition Jean G.Van Bladel IEEE Antennas and Propagation Society, Sponsor IEEE Press Series on ElectromagneticWaveTheory DonaldG.Dudley,SeriesEditor IEEEPRESS “ffirs” — 2007/5/4 — page iii — #3 IEEEPress 445HoesLane Piscataway,NJ08854 IEEEPressEditorialBoard MohamedE.El-Hawary,EditorinChief R.Abari T.G.Croda R.J.Herrick S.Basu S.Farshchi M.S.Newman A.Chatterjee S.V.Kartalopoulous N.Schulz T.Chen B.M.Hammerli KennethMoore,DirectorofIEEEBookandInformationServices(BIS) CatherineFaduska,SeniorAcquisitionsEditor JeanneAudino,ProjectEditor IEEEAntennasandPropagationSociety,Sponsor IEEEAPSLiaisontoIEEEPress,RobertMailloux TechnicalReviewers ChalmersM.Butler,ClemsonUniversity RobertE.Collin,CaseWesternReserveUniversity DonaldG.Dudley,UniversityofArizona EhudHeyman,TelAvivUniversity AkiraIshimaru,UniversityofWashington DouglasS.Jones,UniversityofDundee Copyright©2007bytheInstituteofElectricalandElectronicsEngineers,Inc. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.Allrightsreserved. PublishedsimultaneouslyinCanada. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyany means,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection 107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,or authorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222 RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.com. RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons, Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008,oronlineat http://www.wiley.com/go/permission. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing thisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsof thisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.No warrantymaybecreatedorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceandstrategies containedhereinmaynotbesuitableforyoursituation.Youshouldconsultwithaprofessionalwhereappropriate. Neitherthepublishernorauthorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbut notlimitedtospecial,incidental,consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactourCustomer CareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat(317)572-3993orfax (317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationDataisavailable. ISBN978-0-471-26388-3 PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 “ffirs” — 2007/5/4 — page iv — #4 ToHjördisandSigrid “ffirs” — 2007/5/4 — page v — #5 “ffirs” — 2007/5/4 — page vi — #6 Contents Preface xiii 2.8 DirectNumericalSolutionof MatrixProblems 69 2.9 IterativeNumericalSolution ofMatrixProblems 70 1. LinearAnalysis 1 3. ElectrostaticFieldsinthePresence 1.1 LinearSpaces 2 ofDielectrics 77 1.2 LinearTransformations 5 1.3 TheInversionProblem 8 3.1 VolumeChargesinVacuum 77 1.4 Green’sFunctions 11 3.2 Green’sFunctionfor 1.5 Reciprocity 14 InfiniteSpace 80 1.6 Green’sDyadics 17 3.3 MultipoleExpansion 83 1.7 ConvergenceofaSeries 19 3.4 PotentialGeneratedbya 1.8 Eigenfunctions 20 SingleLayerofCharge 86 1.9 IntegralOperators 23 3.5 PotentialGeneratedbya 1.10 EigenfunctionExpansions 26 DoubleLayerofCharge 91 1.11 Discretization 30 3.6 PotentialGeneratedbya 1.12 Matrices 33 LinearCharge 94 1.13 SolutionofMatrixEquations: 3.7 SphericalHarmonics 98 Stability 36 1.14 FiniteDifferences 38 3.8 DielectricMaterials 102 1.15 Perturbations 43 3.9 CavityFields 105 3.10 DielectricSphereinan ExternalField 108 2. VariationalTechniques 51 3.11 DielectricSpheroidinan IncidentField 111 2.1 Stationaryfunctionals 52 3.12 NumericalMethods 115 2.2 ASuitableFunctionalforthe StringProblem 53 2.3 FunctionalsfortheGeneral 4. ElectrostaticFieldsinthePresence LTransformation 55 ofConductors 125 2.4 Euler’sEquationsofSome ImportantFunctionals 58 4.1 Conductivity 125 2.5 DiscretizationoftheTrial 4.2 PotentialOutsidea Functions 60 ChargedConductor 127 2.6 SimpleFiniteElementsfor 4.3 CapacitanceMatrix 133 PlanarProblems 62 4.4 TheDirichletProblem 134 2.7 MoreFiniteElements 65 4.5 TheNeumannProblem 137 vii “ftoc” — 2007/4/12 — page vii — #1