Electromagnetic field theory

203 Pages·2004·1.315 MB·English

by  Harald J. W. Muller-Kirsten

Electromagnetic
Field Theory
BO THIDÉ
(cid:7)
UPSILON BOOKS

ELECTROMAGNETIC FIELD THEORY

Electromagnetic
Field Theory
BO THIDÉ
SwedishInstituteofSpacePhysics
and
DepartmentofAstronomyandSpacePhysics
UppsalaUniversity,Sweden
and
SchoolofMathematicsandSystemsEngineering
VäxjöUniversity,Sweden
(cid:7)
UPSILON BOOKS COMMUNA AB UPPSALA SWEDEN
(cid:1) (cid:1) (cid:1)
Alsoavailable
ELECTROMAGNETICFIELD THEORY
EXERCISES
by
TobiaCarozzi,AndersEriksson,BengtLundborg,
BoThidéandMattiasWaldenvik
Freelydownloadablefrom
www.plasma.uu.se/CED
This book was typeset in LATEX2" (based on TEX 3.14159 and Web2C 7.4.2) on an
HPVisualize9000⁄360workstationrunningHP-UX11.11.
Copyright c1997,1998,1999,2000,2001,2002,2003and2004by
(cid:13)
BoThidé
Uppsala,Sweden
Allrightsreserved.
ElectromagneticFieldTheory
ISBNX-XXX-XXXXX-X
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Preface
ThecurrentbookisanoutgrowthofthelecturenotesthatIpreparedforthefour-credit
courseElectrodynamicsthatwasintroducedintheUppsalaUniversitycurriculumin
1992, to becomethe five-credit course ClassicalElectrodynamicsin 1997. To some
extent, parts of these notes were based on lecture notes prepared, in Swedish, by
BENGT LUNDBORG whocreated,developedandtaughttheearlier, two-creditcourse
ElectromagneticRadiationatourfaculty.
Intendedprimarilyasatextbookforphysicsstudentsattheadvancedundergradu-
ate or beginning graduate level, it is hoped that the present book may be useful for
researchworkerstoo. Itprovidesathoroughtreatmentofthetheoryofelectrodynam-
ics, mainly from a classical field theoretical point of view, and includes such things
as formal electrostatics and magnetostatics and their unification into electrodynam-
ics, the electromagnetic potentials, gauge transformations, covariant formulation of
classicalelectrodynamics,force,momentumandenergyoftheelectromagneticfield,
radiationandscatteringphenomena,electromagneticwavesandtheirpropagationin
vacuumand inmedia, andcovariantLagrangian/Hamiltonianfield theoretical meth-
ods for electromagnetic fields, particles andinteractions. The aim has been to write
abookthatcanservebothasanadvancedtextinClassicalElectrodynamicsandasa
preparationforstudiesinQuantumElectrodynamicsandrelatedsubjects.
In an attempt to encourage participation by other scientists and students in the
authoringofthisbook,andtoensureitsqualityandscopetomakeitusefulinhigher
university education anywhere in the world, it was produced within a World-Wide
Web(WWW)project. Thisturnedouttobearathersuccessfulmove. Bymakingan
electronicversionofthebookfreelydown-loadableonthenet,commentshavebeen
onlyreceivedfromfellowInternetphysicistsaroundtheworldandfromWWW‘hit’
statistics it seems that the book serves as a frequently used Internet resource. This
wayitishopedthatitwillbeparticularlyusefulforstudentsandresearchersworking
underfinancialorothercircumstancesthatmakeitdi(cid:14)culttoprocureaprintedcopy
ofthebook.
ThanksareduenotonlytoBengtLundborgforprovidingtheinspirationtowrite
thisbook,butalsotoprofessorCHRISTERWAHLBERGandprofessorGÖRANFÄLDT,
Uppsala University, and professor YAKOV ISTOMIN, Lebedev Institute, Moscow, for
interestingdiscussionsonelectrodynamicsandrelativityingeneralandonthisbookin
particular. Commentsfromformergraduatestudents MATTIAS WALDENVIK, TOBIA
CAROZZI and ROGER KARLSSON as well as ANDERS ERIKSSON, all at the Swedish
Institute of Space Physics in Uppsala and who all have participated in the teaching,
vii
PREFACE
on the material coveredin the course and in this book are gratefully acknowledged.
Thanks are also due to my long-term space physics colleague HELMUT KOPKA of
the Max-Planck-Institut für Aeronomie, Lindau, Germany, who not only taught me
about the practical aspects of the of high-power radio wave transmitters and trans-
mission lines, but also about the more delicate aspects of typesetting a book in TEX
andLATEX. IamparticularlyindebtedtoAcademicianprofessor VITALIY LAZAREV-
ICH GINZBURG, 2003 Nobel Laureate in Physics, for his many fascinating and very
elucidatinglectures,commentsandhistoricalfootnotesonelectromagneticradiation
whilecruisingontheVolgariveratourjointRussian-Swedishsummerschoolsduring
the1990sandfornumerousprivatediscussions.
Finally,IwouldliketothankallstudentsandInternetuserswhohavedownloaded
andcommentedonthebookduringitslifeontheWorld-WideWeb.
Uppsala,Sweden BOTHIDÉ
January,2004
viii
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Contents
Preface vii
Contents ix
ListofFigures xiii
1 ClassicalElectrodynamics 1
1.1 Electrostatics 2
1.1.1 Coulomb’slaw 2
1.1.2 Theelectrostaticfield 3
1.2 Magnetostatics 6
1.2.1 Ampère’slaw 6
1.2.2 Themagnetostaticfield 7
1.3 Electrodynamics 9
1.3.1 Equationofcontinuityforelectriccharge 9
1.3.2 Maxwell’sdisplacementcurrent 10
1.3.3 Electromotiveforce 10
1.3.4 Faraday’slawofinduction 11
1.3.5 Maxwell’smicroscopicequations 14
1.3.6 Maxwell’smacroscopicequations 14
1.4 Electromagneticduality 15
1.5 Bibliography 22
2 ElectromagneticWaves 25
2.1 Thewaveequations 26
2.1.1 ThewaveequationforE 26
2.1.2 ThewaveequationforB 26
2.1.3 Thetime-independentwaveequationforE 27
2.2 Planewaves 30
2.2.1 Telegrapher’sequation 31
2.2.2 Wavesinconductivemedia 32
2.3 Observablesandaverages 33
ix
CONTENTS
2.4 Bibliography 34
3 ElectromagneticPotentials 35
3.1 Theelectrostaticscalarpotential 35
3.2 Themagnetostaticvectorpotential 36
3.3 Theelectrodynamicpotentials 36
3.3.1 Lorenz-Lorentzgauge 38
3.3.2 Coulombgauge 42
3.3.3 Gaugetransformations 42
3.4 Bibliography 45
4 RelativisticElectrodynamics 47
4.1 Thespecialtheoryofrelativity 47
4.1.1 TheLorentztransformation 48
4.1.2 Lorentzspace 49
4.1.3 Minkowskispace 54
4.2 Covariantclassicalmechanics 57
4.3 Covariantclassicalelectrodynamics 58
4.3.1 Thefour-potential 58
4.3.2 TheLiénard-Wiechertpotentials 59
4.3.3 Theelectromagneticfieldtensor 61
4.4 Bibliography 64
5 ElectromagneticFieldsandParticles 67
5.1 Chargedparticlesinanelectromagneticfield 67
5.1.1 Covariantequationsofmotion 67
5.2 Covariantfieldtheory 73
5.2.1 Lagrange-Hamiltonformalismforfieldsandinteractions 73
5.3 Bibliography 81
6 ElectromagneticFieldsandMatter 83
6.1 Electricpolarisationanddisplacement 83
6.1.1 Electricmultipolemoments 83
6.2 Magnetisationandthemagnetisingfield 86
6.3 Energyandmomentum 88
6.3.1 TheenergytheoreminMaxwell’stheory 88
6.3.2 ThemomentumtheoreminMaxwell’stheory 89
6.4 Bibliography 91
7 ElectromagneticFieldsfromArbitrarySourceDistributions 93
7.1 Themagneticfield 95
7.2 Theelectricfield 96
7.3 Theradiationfields 99
x
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