Lecture Notes in Physics Arnab Rai Choudhuri Advanced Electromagnetic Theory Lecture Notes in Physics FoundingEditors WolfBeiglböck JürgenEhlers KlausHepp Hans-ArwedWeidenmüller Volume 1009 SeriesEditors RobertaCitro,Salerno,Italy PeterHänggi,Augsburg,Germany MortenHjorth-Jensen,Oslo,Norway MaciejLewenstein,Barcelona,Spain AngelRubio,Hamburg,Germany WolfgangSchleich,Ulm,Germany StefanTheisen,Potsdam,Germany JamesD.Wells,AnnArbor,MI,USA GaryP.Zank,Huntsville,AL,USA The series Lecture Notes in Physics (LNP), founded in 1969, reports new developmentsinphysicsresearchandteaching-quicklyandinformally,butwitha highqualityandtheexplicitaimtosummarizeandcommunicatecurrentknowledge in an accessible way. 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Proposals should be sent to a member of the Editorial Board, or directly to the responsibleeditoratSpringer: DrLisaScalone SpringerNature Physics Tiergartenstrasse17 69121Heidelberg,Germany [email protected] Arnab Rai Choudhuri Advanced Electromagnetic Theory ArnabRaiChoudhuri DepartmentofPhysics IndianInstituteofScience Bangalore,India ISSN 0075-8450 ISSN 1616-6361 (electronic) LectureNotesinPhysics ISBN 978-981-19-5943-1 ISBN 978-981-19-5944-8 (eBook) https://doi.org/10.1007/978-981-19-5944-8 ©SpringerNatureSingaporePteLtd.2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore To OpuandTipu Preface Thisbookisbasedonaone-semestercourseonelectromagnetictheoryatadvanced undergraduateorbeginninggraduatelevelwhichIhavetaughtattheIndianInstitute ofScienceseveraltimes.Aprerequisiteforthiscourseisamoreelementarycourseat thelevelofPurcell’sElectricityandMagnetism,teachingstudentshowtoformulate thebasicprinciplesofelectromagnetismthroughvectorialequations.Theadvanced course on which this book is based is the last course on classical electrodynamics takenbyourgraduatestudentsbeforetheyembarkonresearchindifferentbranches ofphysics.Theaimofthiscourseistoexposestudentstoalltheimportantbasicprin- ciplesofthesubjectwhichprofessionalphysicistsworkinginanyareaoftheoretical orexperimentalphysicsareexpectedtoknow. Teaching a course on electromagnetic theory at the level of this book is quite challenging due to the wide diversity of topics which are expected to be covered. Ontheonehand,therearecertainpracticaltopicswhichhaveextensiveengineering applications,suchasthetheoryofwaveguidesandantennae.Ontheotherhand,one hastocoverothertopicswhicharegatewaystoadvancedtheoreticalphysics,suchas therelationofelectromagnetictheorywithspecialrelativityandtheactionprinciple formulation in a Lorentz-invariant manner. Additionally, there are topics like the calculation of electromagnetic fields from the Liénard–Wiechert potentials, which involve mathematical derivations more complicated than probably any derivations whichstudentsatthislevelarelikelytoencounterinotherbasicphysicscourses.I have tried my best to write a balanced book which should be suitable for students goingintodifferentbranchesoftheoreticalorexperimentalphysics.Imaybeslightly biasedbymypersonalresearchinterestinplasmaastrophysics,butIbelievethatI have kept this bias within acceptable limits by adding only a short chapter on the basicsofplasmaphysicsattheendofthisbook.Apartfromthegrowingimportance of plasma physics, I firmly believe that even from a conceptual point of view it is desirablethatallphysicsstudentsshouldhavesomeideaaboutthebasicsofplasma physics—themany-bodytheoryofclassicalelectrodynamics. Althoughmostofthebasicprinciplesofelectromagnetictheorycoveredinabook likethiswereestablishedmorethanacenturyagoandhavenotchangedsincethen, therehavebeenmanychangesinthelastfewdecadesinthewaytheseprinciplesare vii viii Preface taughtattheadvancedundergraduateorthebeginninggraduatelevel.WhenIwas goingtograduateschoolinthe1980s,itwascustomaryformanyuniversitiesaround the world (especially American universities) to teach electromagnetic theory in a leisurelymanneroverayear(intwosemestersorthreequarters).Veryoften,there would not be a separate course on mathematical methods of physics, and students wereexpectedtobetaughtatleastsomebasictechniquesofmathematicalmethodsin theelectromagnetictheorycourse.Onetextbookwhichheldundisputedswayinthat erawasJackson’sClassicalElectrodynamics.Ibelongtothegenerationofphysicists whowere‘raised’onJackson’sbook.Withtremendousadvancesindifferentareas ofphysicsoverthelastfewdecades,ithasnowbecomeimperativetogivestudents some exposure to these modern topics at a stage sufficiently early in their career. Thiscanonlybedonebycuttingoutsomepartsoftheoldercurriculum.Whileany competentphysicistwouldagreethatitisnotpossibletobecomeagoodphysicist withoutagoodcommandoftheolderclassicalareasofphysics,itisalsogenerally agreedthatperhapsnoteverytopicintheseolderareasofphysicswhichusedtobe taughttoallphysicsstudentsafewdecadesagoneedstobetaughttoday.Onecan prunetheoldercurriculumtoretainonlytheessentialswhicheveryphysicsstudent oughttoknow.Manyuniversitiesaroundtheworldnowofferaone-semestercourse ofelectromagnetictheoryattheadvancedundergraduateorthebeginninggraduate level,ratherthanayear-longsequenceofcourses. Manyoftheoldertextbooksofelectromagnetictheorywerewrittenwiththeaimof teachingthesubjectoverayear(thethirdeditionofJackson’sbookrunstoabout800 pages).Incontrast,myaimhasbeentowritealeanandthinadvancedelectromagnetic theorytextbookfromamodernperspectivewhichcoversalltheimportanttopicsthat aprofessionalphysicistneedstoknowandwhichcanbecoveredcomfortablyina one-semestercourse.Therebeingmanytextbookswithamorecompletecoverageof thesubject,Ihavenotfelttheneedtostriveforcompleteness.Thisbookessentially coversthematerialswhichIwouldmanagetoteachinaone-semestercourseatthe IndianInstituteofScience,lecturingthreehoursperweek.AlthoughIamconsidered a reasonably fast teacher, I trust that a teacher proceeding at a moderate pace will beabletocoveralargepartofthisbook.Whiledesigningthiscourse,Ihadtobe ruthlesslyselectiveindecidingwhichtopicsofelectromagnetictheoryaprofessional physicistmustknowfromthelastcourseonthesubject.Althoughnoteverybodycan beexpectedtobein100%agreementwithme,Idobelievethatanyprofessorwhois compelledtoteachtheessentialsofadvancedelectromagnetictheoryinonesemester inabalancedcoursesuitableforallphysicsstudentswillhavetoendupwithacourse notverydifferentfromwhatispresentedinthisbook.Whiledecidingwhichtopics toincludeandwhichtopicstoleaveout,Ihadoneguidingprinciple.Igaveahigher prioritytotopicswhichintroduceimportantnewconceptsratherthantopicswhich are more like detailed working out of already established concepts. For example, althoughIdiscussedtwo-dimensionalboundaryvalueproblemsinelectrostaticsin considerable detail, I left out three-dimensional problems and thereby saved some precioustimewhichcouldbeusedforteachingothertopicswhichIconsideredmore important. Preface ix Atime-honouredpracticefollowedinmanyofthestandardtextbooksofelectro- magnetictheoryhadbeentoprovideanextensivesetofexerciseproblems.Jackson’s bookisfamous(ornotorious,dependingonyourpointofview!)foritscollectionof difficultproblems.Inkeepingwiththeoverallspiritofthebook,Ihaveincludeda limitednumberofexerciseproblemsspecificallyselectedforadvancingthestudent’s understandingofthematerialsdiscussedinthetext.Ihaveavoidedproblemsforthe sole purpose of testing a student’s capacity for intellectual gymnastics at its limit. Thereisanothertrickyissueconnectedwithexerciseproblems:ascribingthecorrect creditto thepersons who might have firstinvented some of these problems.Since thisisimpossibletodo,IherebydeclarethatIcollectedmanyoftheproblemsfrom differentsourcesovertheyears(Icannotevenrecallnowwhichproblemmighthave beentakenfromwhere)andImakenoclaimofmyintellectualownershipoverthe exerciseproblems. Whilethethoughtofwritingthisbookhasbeenonmymindforseveralyears,Iat lastgottheforcedopportunityofworkingonthisbookduringtheseveraldepressing monthswhenmuchoftheworld—especiallymycountryIndia—wasunderalmost completelockdownduetotheCOVID-19pandemic.Workingonthisbookhelped metomaintainmymentalsanityatthisdifficulttime.Ihavenaturallybeeninfluenced bymanyauthorswhowrotebooksonthissubjectbeforeme.Inparticular,Iexpress myindebtednesstoFeynman,Griffiths,Jackson,LandauandLifshitz,Panofskyand Phillips. I am grateful to many students who have taken this course from me over theyearsandencouragedmethroughtheirquestionsandfeedback.Ihavealsohad fruitful discussions with many departmental colleagues about the teaching of this course.Iwouldparticularlyliketomentiontwoyoungercolleagueswhohadtaught this course in our department many times like me and who were very enthusiastic aboutmyideaofwritingthisbook,butwhoarenolongeramongustoseethisbook: Vasant Natarajan and V. Venkataraman. I thank Bibhuti Kumar Jha for preparing most of the figures in this book. Finally, the book would not have been possible withoutthecontinuoussupportofmywifeMahua. Bangalore,India ArnabRaiChoudhuri