P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 Modern Electrodynamics Anengagingwritingstyleandastrongfocusonthephysicsmakethiscomprehensive,graduate-level textbookuniqueamongexistingclassicalelectromagnetismtextbooks. Chargedparticlesinvacuumandtheelectrodynamicsofcontinuousmediaaregivenequalattention in discussions of electrostatics, magnetostatics, quasistatics, conservation laws, wave propagation, radiation,scattering,specialrelativity,andfieldtheory.Extensiveuseofqualitativeargumentssimilar tothoseusedbyworkingphysicistsmakesModernElectrodynamicsamust-haveforeverystudentof thissubject. In24chapters,thetextbookcoversmanymoretopicsthancanbepresentedinatypicaltwo-semester course, making it easy for instructors to tailor courses to their specific needs. Close to 120 worked examples and 60 applications boxes help the reader build physical intuition and develop technical skill.Nearly600end-of-chapterhomeworkproblemsencouragestudentstoengageactivelywiththe material.Asolutionsmanualisavailableforinstructorsatwww.cambridge.org/Zangwill. Andrew Zangwill is a Professor of Physics at the Georgia Institute of Technology, with research interestsintheoreticalcondensedmatterphysics.HeistheauthorofthepopulartextbookPhysicsat Surfaces(CambridgeUniversityPress,1988)andhastaughtclassicalelectromagnetismatthegraduate andundergraduatelevelsfor20years. FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 Modern Electrodynamics ANDREW ZANGWILL SchoolofPhysics GeorgiaInstituteofTechnology FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 cambridge university press Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,Sa˜oPaulo,Delhi,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/Zangwill (cid:2)C A.Zangwill2012 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2012 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata ISBN978-0-521-89697-9Hardback Additionalresourcesforthispublicationatwww.cambridge.org/Zangwill CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredtoin thispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis, orwillremain,accurateorappropriate. FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 Therearemorethingsinheaven&earthconnectedwithelectromagnetismthanare yetdream’tofinphilosophy. JosephHenry,lettertoLewisC.Beck(1827) ReprintedfromThePapersofJosephHenry,VolumeI,editedbyNathanReingold (Washington,DC:SmithsonianInstitutionPress).Usedbypermissionofthe SmithsonianInstitution.Copyright1972. Thesearchforreasonendsattheshoreoftheknown;ontheimmenseexpanse beyonditonlytheineffablecanglide. AbrahamJoshuaHeschel,ManisNotAlone(1951) Whyrepeatallthis?Becausetherearenewgenerationsborneveryday.Because therearegreatideasdevelopedinthehistoryofman,andtheseideasdonotlast unlesstheyarepassedpurposelyandclearlyfromgenerationtogeneration. RichardFeynman,TheMeaningofItAll(1963) FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 Contents ListofApplications pagexiv Preface xix 1 MathematicalPreliminaries 1 1.1 Introduction 1 1.2 Vectors 1 1.3 Derivatives 7 1.4 Integrals 9 1.5 GeneralizedFunctions 11 1.6 FourierAnalysis 15 1.7 OrthogonalTransformations 18 1.8 CartesianTensors 20 1.9 TheHelmholtzTheorem 22 1.10 LagrangeMultipliers 24 Sources,References,andAdditionalReading 24 Problems 25 2 TheMaxwellEquations 29 2.1 Introduction 29 2.2 TheMaxwellEquationsinVacuum 33 2.3 Microscopicvs.Macroscopic 38 2.4 TheMaxwellEquationsinMatter 43 2.5 QuantumLimitsandNewPhysics 46 2.6 SIUnits 50 2.7 AHeuristicDerivation 51 Sources,References,andAdditionalReading 53 Problems 55 3 Electrostatics 58 3.1 Introduction 58 3.2 Coulomb’sLaw 59 3.3 TheScalarPotential 60 3.4 Gauss’LawandSolidAngle 68 3.5 ElectrostaticPotentialEnergy 74 3.6 ElectrostaticTotalEnergy 76 3.7 TheElectricStressTensor 81 Sources,References,andAdditionalReading 84 Problems 85 FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 viii CONTENTS 4 ElectricMultipoles 90 4.1 Introduction 90 4.2 TheElectricDipole 92 4.3 ElectricDipoleLayers 98 4.4 TheElectricQuadrupole 102 4.5 SphericalMathematics 106 4.6 SphericalandAzimuthalMultipoles 109 4.7 PrimitiveandTracelessMultipoleMoments 116 Sources,References,andAdditionalReading 119 Problems 121 5 ConductingMatter 126 5.1 Introduction 126 5.2 ElectrostaticInduction 126 5.3 ScreeningandShielding 133 5.4 Capacitance 134 5.5 TheEnergyofaSystemofConductors 142 5.6 ForcesonConductors 143 5.7 RealConductors 149 Sources,References,andAdditionalReading 151 Problems 152 6 DielectricMatter 158 6.1 Introduction 158 6.2 Polarization 158 6.3 TheFieldProducedbyPolarizedMatter 162 6.4 TheTotalElectricField 165 6.5 SimpleDielectricMatter 167 6.6 ThePhysicsoftheDielectricConstant 175 6.7 TheEnergyofDielectricMatter 178 6.8 ForcesonDielectricMatter 184 Sources,References,andAdditionalReading 191 Problems 193 7 Laplace’sEquation 197 7.1 Introduction 197 7.2 PotentialTheory 198 7.3 Uniqueness 199 7.4 SeparationofVariables 201 7.5 CartesianSymmetry 203 7.6 AzimuthalSymmetry 209 7.7 SphericalSymmetry 212 7.8 CylindricalSymmetry 215 7.9 PolarCoordinates 218 7.10 TheComplexPotential 221 7.11 AVariationalPrinciple 226 Sources,References,andAdditionalReading 228 Problems 229 FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 CONTENTS ix 8 Poisson’sEquation 236 8.1 Introduction 236 8.2 TheKeyIdea:Superposition 236 8.3 TheMethodofImages 237 8.4 TheGreenFunctionMethod 250 8.5 TheDirichletGreenFunction 252 8.6 TheComplexLogarithmPotential 260 8.7 ThePoisson-BoltzmannEquation 262 Sources,References,andAdditionalReading 264 Problems 265 9 SteadyCurrent 272 9.1 Introduction 272 9.2 CurrentinVacuum 273 9.3 CurrentinMatter 275 9.4 PotentialTheoryforOhmicMatter 276 9.5 ElectricalResistance 277 9.6 JouleHeating 280 9.7 ElectromotiveForce 282 9.8 CurrentSources 287 9.9 DiffusionCurrent:Fick’sLaw 291 Sources,References,andAdditionalReading 293 Problems 294 10 Magnetostatics 301 10.1 Introduction 301 10.2 TheLawofBiotandSavart 304 10.3 Ampe`re’sLaw 307 10.4 TheMagneticScalarPotential 312 10.5 TheVectorPotential 320 10.6 TheTopologyofMagneticFieldLines 325 Sources,References,andAdditionalReading 329 Problems 330 11 MagneticMultipoles 336 11.1 Introduction 336 11.2 TheMagneticDipole 337 11.3 MagneticDipoleLayers 345 11.4 ExteriorMultipoles 346 11.5 InteriorMultipoles 353 11.6 AxiallySymmetricMagneticFields 357 Sources,References,andAdditionalReading 359 Problems 361 12 MagneticForceandEnergy 365 12.1 Introduction 365 12.2 ChargedParticleMotion 366 FOR ENDORSEMENT PURPOSES ONLY. DO NOT DISTRIBUTE P1:SFK Trim:246mm×189mm Top:10.544mm Gutter:18.98mm CUUK1954-FM CUUK1954/Zangwill 9780521896979 August10,2012 13:53 x CONTENTS 12.3 TheForcebetweenSteadyCurrents 368 12.4 TheMagneticDipole 372 12.5 TheMagneticStressTensor 381 12.6 MagnetostaticTotalEnergy 384 12.7 MagnetostaticPotentialEnergy 389 12.8 Inductance 394 Sources,References,andAdditionalReading 399 Problems 401 13 MagneticMatter 407 13.1 Introduction 407 13.2 Magnetization 407 13.3 TheFieldProducedbyMagnetizedMatter 412 13.4 FictitiousMagneticCharge 415 13.5 TheTotalMagneticField 419 13.6 SimpleMagneticMatter 421 13.7 TheEnergyofMagneticMatter 433 13.8 ForcesonMagneticMatter 435 13.9 PermanentMagneticMatter 443 Sources,References,andAdditionalReading 447 Problems 448 14 DynamicandQuasistatic Fields 455 14.1 Introduction 455 14.2 TheAmpe`re-MaxwellLaw 456 14.3 Faraday’sLaw 460 14.4 ElectromagneticInduction 462 14.5 SlowlyTime-VaryingChargeinVacuum 467 14.6 SlowlyTime-VaryingCurrentinVacuum 470 14.7 QuasistaticFieldsinMatter 472 14.8 PoorConductors:Quasi-Electrostatics 473 14.9 GoodConductors:Quasi-Magnetostatics 475 14.10 TheSkinEffect 477 14.11 MagneticDiffusion 481 14.12 Eddy-CurrentPhenomena 483 14.13 ACCircuitTheory 486 Sources,References,andAdditionalReading 493 Problems 494 15 GeneralElectromagneticFields 501 15.1 Introduction 501 15.2 Symmetry 501 15.3 ElectromagneticPotentials 503 15.4 ConservationofEnergy 507 15.5 ConservationofLinearMomentum 511 15.6 ConservationofAngularMomentum 516 15.7 TheCenterofEnergy 519 15.8 ConservationLawsinMatter 522 FOR ENDORSEMENT PURPOSES ONLY. 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