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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.
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Modern
Electrodynamics
ANDREW ZANGWILL
SchoolofPhysics
GeorgiaInstituteofTechnology
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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.
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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)
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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
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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
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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
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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
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