Theoretical Physics 3: Electrodynamics

675 Pages·2016·5.637 MB·English

by  Wolfgang Nolting

Wolfgang Nolting
Theoretical
Physics 3
Electrodynamics
Theoretical Physics 3

Wolfgang Nolting
Theoretical Physics 3
Electrodynamics
123
WolfgangNolting
Inst.Physik
Humboldt-UniversitaRtzuBerlin
Berlin,Germany
ISBN978-3-319-40167-6 ISBN978-3-319-40168-3 (eBook)
DOI10.1007/978-3-319-40168-3
LibraryofCongressControlNumber:2016943655
©SpringerInternationalPublishingSwitzerland2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland
General Preface
ThesevenvolumesoftheseriesBasicCourse:TheoreticalPhysicsarethoughttobe
textbookmaterialforthestudyofuniversity-levelphysics.Theyareaimedtoimpart,
in a compact form, the most important skills of theoretical physics which can be
usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced
study of physics as well as in the subsequent physics research. The conceptual
designofthepresentationisorganizedinsuchawaythat
ClassicalMechanics(volume1)
AnalyticalMechanics(volume2)
Electrodynamics(volume3)
SpecialTheoryofRelativity(volume4)
Thermodynamics(volume5)
are considered as the theory part of an integrated course of experimental and
theoretical physics as is being offered at many universities starting from the first
semester.Therefore,thepresentationisconsciouslychosentobeveryelaborateand
self-contained,sometimessurelyatthe costofcertainelegance,sothatthecourse
is suitableevenforself-study,at firstwithoutanyneedof secondaryliterature.At
anystage,nomaterialisusedwhichhasnotbeendealtwithearlierinthetext.This
holds in particular for the mathematical tools, which have been comprehensively
developed starting from the school level, of course more or less in the form of
recipes,suchthatrightfromthebeginningofthestudy,onecansolveproblemsin
theoreticalphysics. The mathematicalinsertionsare always then pluggedin when
theybecomeindispensabletoproceedfurtherintheprogramoftheoreticalphysics.
Itgoeswithoutsayingthatinsuchacontext,notallthemathematicalstatementscan
be proved and derived with absolute rigour. Instead, sometimes a reference must
be made to an appropriate course in mathematics or to an advanced textbook in
mathematics. Nevertheless, I have tried for a reasonably balanced representation
so that the mathematical tools are not only applicable but also appear at least
‘plausible’.
Themathematicalinterludesareofcoursenecessaryonlyinthefirstvolumesof
this series, which incorporatemore or less the materialof a bachelorprogramme.
v
vi GeneralPreface
Inthesecondpartoftheserieswhichcomprisesthemodernaspectsoftheoretical
physics,
QuantumMechanics:Basics(volume6)
QuantumMechanics:MethodsandApplications(volume7)
StatisticalPhysics(volume8)
Many-BodyTheory(volume9),
mathematicalinsertionsarenolongernecessary.Thisispartlybecause,bythetime
onecomestothisstage,theobligatorymathematicscoursesonehastotakeinorder
to study physics would have provided the required tools. The fact that training in
theory has already started in the first semester itself permits inclusion of parts of
quantum mechanics and statistical physics in the bachelor programme itself. It is
clear that the content of the last three volumes cannot be part of an integrated
coursebutratherthesubjectmatterofpuretheorylectures.Thisholdsinparticular
forMany-BodyTheory whichis offered,sometimesunderdifferentnamesas, e.g.
advancedquantummechanics,intheeighthorsosemesterofstudy.Inthispart,new
methodsandconceptsbeyondbasicstudiesareintroducedanddiscussedwhichare
developedinparticularforcorrelatedmanyparticlesystemswhichinthemeantime
havebecomeindispensablefora studentpursuingmaster’sora higherdegreeand
forbeingabletoreadcurrentresearchliterature.
In all the volumes of the series Basic Course: Theoretical Physics, numerous
exercisesareincludedtodeepentheunderstandingandtohelpcorrectlyapplythe
abstractlyacquiredknowledge.Itisobligatoryforastudenttoattemptonhisown
to adapt and apply the abstract concepts of theoretical physics to solve realistic
problems.Detailed solutionsto the exercisesare givenat the endof eachvolume.
The idea is to help a student to overcomeany difficulty at a particular step of the
solutionortocheckone’sowneffort.Importantlythesesolutionsshouldnotseduce
thestudenttofollowtheeasywayoutasasubstituteforhisowneffort.Attheend
of each biggerchapter,I have addedself-examinationquestionswhich shall serve
asaself-testandmaybeusefulwhilepreparingforexaminations.
I should not forget to thank all the people who have contributed one way or
an other to the success of the book series. The single volumes arose mainly from
lectures which I gave at the universities of Muenster, Wuerzburg, Osnabrueck,
and Berlin in Germany, Valladolid in Spain, and Warangal in India. The interest
and constructivecriticism of the students providedme the decisive motivationfor
preparing the rather extensive manuscripts. After the publication of the German
version,Ireceivedalotofsuggestionsfromnumerouscolleaguesforimprovement,
and this helped to further develop and enhance the concept and the performance
of the series. In particular, I appreciate very much the support by Prof. Dr. A.
Ramakanth,a long-standingscientific partnerand friend,who helpedme in many
respects,e.g.whatconcernsthecheckingofthetranslationoftheGermantextinto
thepresentEnglishversion.
GeneralPreface vii
SpecialthanksareduetotheSpringercompany,inparticulartoDr.Th.Schneider
and his team. I remember many useful motivations and stimulations. I have the
feelingthatmybooksarewelltakencareof.
Berlin,Germany WolfgangNolting
May2015

Preface to Volume 3
The main goal of this volume 3 (Electrodynamics) corresponds exactly to that of
the total Basic Course: Theoretical Physics. It is thought to be an accompanying
textbookmaterialforthestudyofuniversity-levelphysics.Itisaimedtoimpart,ina
compactform,themostimportantskillsoftheoreticalphysicswhichcanbeusedas
basisforhandlingmoresophisticatedtopicsandproblemsintheadvancedstudyof
physicsaswellasinthesubsequentphysicsresearch.Itispresentedinsuchaway
thatitenablesself-studywithouttheneedforademandingandlaboriousreference
to secondaryliterature. For the understandingof the text, it is only presumedthat
thereaderhasagoodgraspofwhathasbeenelaboratedintheprecedingvolumes1
and 2. Mathematical interludes are always presented in a compact and functional
formandpracticedwhentheyappearindispensableforfurtherdevelopmentofthe
theory.Forthewholetext,itholdsthatIhadtofocusontheessentials,presenting
them in a detailed and elaborate form, sometimes consciously sacrificing certain
elegance.Itgoeswithoutsayingthatafterthe basic course,secondaryliteratureis
neededtodeepentheunderstandingofphysicsandmathematics.
Electrodynamics is presented here in its inductive version. That means that
the fundamental Maxwell equations are motivated by some basic and consistent
experimentalfacts.TheconclusionsderivedfromtheMaxwellequationscanthenbe
comparedtothecorrespondingexperimentalfacts.Thecompleteagreementfound
up to now provides a strong support of the validity of the concept. The mathe-
matically demanding nature of electrodynamics makes practicing the application
ofconceptsandmethodsespeciallymandatory.Inthiscontext,theexerciseswhich
areofferedafterallimportantsubsectionsplayanindispensableroleforaneffective
learning.Theelaboratesolutionsofexercisesattheendofthebookshouldnotkeep
thelearnerfromanindependenttreatmentoftheproblems,butshouldonlyserveas
acheckupofone’sownefforts.
This volume on electrodynamics arose from lectures I gave at the German
Universitiesin Muenster and Berlin. The animating interest of the students in my
lecturenoteshasinducedmetopreparethetextwithspecialcare.Thisvolumeone
as well as the other volumesis thoughtto be a textbookmaterial for the study of
basicphysics,primarilyintendedforthestudentsratherthanfortheteachers.
ix