Foundations of Applied Electrodynamics

524 Pages·2010·2.88 MB·English

by  Wen Geyi

P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
FOUNDATIONS
OF APPLIED
ELECTRODYNAMICS
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
FOUNDATIONS
OF APPLIED
ELECTRODYNAMICS
WenGeyi
Waterloo,Canada
A John Wiley and Sons, Ltd., Publication
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
Thiseditionfirstpublished2010
(cid:1)C 2010JohnWiley&Sons,Ltd
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto
reuse the copyright material in this book please see our website at www.wiley.com.
TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,
DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform
orbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,
DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailablein
electronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand
productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespective
owners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.Thispublicationisdesignedto
provideaccurateandauthoritativeinformationinregardtothesubjectmattercovered.Itissoldontheunderstandingthat
thepublisherisnotengagedinrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,
theservicesofacompetentprofessionalshouldbesought.
LibraryofCongressCataloging-in-PublicationData
Wen,Geyi.
Foundationsofappliedelectrodynamics/GeyiWen.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-68862-5(cloth)
1.Electrodynamics–Mathematics. I.Title.
QC631.3.W46 2010
537.601(cid:2)51–dc22
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN 978-0-470-68862-5(H/B)
Typesetin10/12ptTimesbyAptaraInc.,NewDelhi,India
PrintedandBoundin
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
Tomy parents
ToJunandLan
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
Contents
Preface xv
1 MaxwellEquations 1
1.1 ExperimentalLaws 2
1.1.1 Coulomb’sLaw 2
1.1.2 Ampe`re’sLaw 5
1.1.3 Faraday’sLaw 9
1.1.4 LawofConservationofCharge 9
1.2 MaxwellEquations,ConstitutiveRelation,andDispersion 10
1.2.1 MaxwellEquationsandBoundaryConditions 11
1.2.2 ConstitutiveRelations 15
1.2.3 WaveEquations 18
1.2.4 Dispersion 20
1.3 TheoremsforElectromagneticFields 22
1.3.1 SuperpositionTheorem 22
1.3.2 CompensationTheorem 23
1.3.3 ConservationofElectromagneticEnergy 23
1.3.4 ConservationofElectromagneticMomentum 25
1.3.5 ConservationofElectromagneticAngularMomentum 27
1.3.6 UniquenessTheorems 27
1.3.7 EquivalenceTheorems 32
1.3.8 Reciprocity 36
1.4 Wavepackets 39
1.4.1 SpatialWavepacketandTemporalWavepacket 40
1.4.2 SignalVelocityandGroupVelocity 42
1.4.3 EnergyDensityforWavepackets 42
1.4.4 EnergyVelocityandGroupVelocity 45
1.4.5 Narrow-bandStationaryStochasticVectorField 47
2 SolutionsofMaxwellEquations 49
2.1 LinearSpaceandLinearOperator 50
2.1.1 LinearSpace,NormedSpaceandInnerProductSpace 50
2.1.2 LinearandMultilinearMaps 52
P1:OTE/OTE/SPH P2:OTE
FM BLBK281-Wen March13,2010 16:38 PrinterName:YettoCome
viii Contents
2.2 ClassificationofPartialDifferentialEquations 54
2.2.1 CanonicalFormofEllipticalEquations 56
2.2.2 CanonicalFormofHyperbolicEquations 57
2.2.3 CanonicalFormofParabolicEquations 57
2.3 ModernTheoryofPartialDifferentialEquations 58
2.3.1 LimitationofClassicalSolutions 58
2.3.2 TheoryofGeneralizedFunctions 60
2.3.3 SobolevSpaces 66
2.3.4 GeneralizedSolutionsofPartialDifferentialEquations 67
2.4 MethodofSeparationofVariables 69
2.4.1 RectangularCoordinateSystem 69
2.4.2 CylindricalCoordinateSystem 70
2.4.3 SphericalCoordinateSystem 71
2.5 MethodofGreen’sFunction 73
2.5.1 FundamentalSolutionsofPartialDifferentialEquations 73
2.5.2 IntegralRepresentationsofArbitraryFields 74
2.5.3 IntegralRepresentationsofElectromagneticFields 78
2.6 PotentialTheory 83
2.6.1 VectorPotential,ScalarPotential,andGaugeConditions 83
2.6.2 HertzVectorsandDebyePotentials 87
2.6.3 JumpRelationsinPotentialTheory 89
2.7 VariationalPrinciples 93
2.7.1 GeneralizedCalculusofVariation 93
2.7.2 LagrangianFormulation 95
2.7.3 HamiltonianFormulation 100
3 EigenvalueProblems 105
3.1 IntroductiontoLinearOperatorTheory 106
3.1.1 CompactOperatorsandEmbeddings 106
3.1.2 ClosedOperators 109
3.1.3 SpectrumandResolventofLinearOperators 110
3.1.4 AdjointOperatorsandSymmetricOperators 112
3.1.5 EnergySpace 114
3.1.6 EnergyExtension,FriedrichsExtensionand
GeneralizedSolution 116
3.2 EigenvalueProblemsforSymmetricOperators 120
3.2.1 Positive-Bounded-BelowSymmetricOperators 120
3.2.2 CompactSymmetricOperators 126
3.3 InteriorElectromagneticProblems 130
3.3.1 ModeTheoryforWaveguides 130
3.3.2 ModeTheoryforCavityResonators 140
3.4 ExteriorElectromagneticProblems 145
3.4.1 ModeTheoryforSphericalWaveguides 145
3.4.2 SingularFunctionsandSingularValues 149
3.5 EigenfunctionsofCurlOperator 150