Electricity and Magnetism New Formulation by Introduction of Superconductivity PDF
Preview Electricity and Magnetism New Formulation by Introduction of Superconductivity
Undergraduate Lecture Notes in Physics Teruo Matsushita Electricity and Magnetism New Formulation by Introduction of Superconductivity Undergraduate Lecture Notes in Physics Forfurthervolumes: http://www.springer.com/series/8917 UndergraduateLectureNotesinPhysics(ULNP)publishesauthoritativetextscov- eringtopicsthroughoutpureandappliedphysics.Eachtitleintheseriesissuitable as a basis for undergraduate instruction, typically containing practice problems, workedexamples,chaptersummaries,andsuggestionsforfurtherreading. ULNPtitlesmustprovideatleastoneofthefollowing: (cid:2) An exceptionally clear and concise treatment of a standard undergraduate subject. (cid:2) Asolidundergraduate-levelintroductiontoagraduate,advanced,ornonstandard subject. (cid:2) Anovelperspectiveoranunusualapproachtoteachingasubject. ULNPespeciallyencouragesnew,original,andidiosyncraticapproachestophysics teachingattheundergraduatelevel. ThepurposeofULNPisto provideintriguing,absorbingbooksthatwillcontinue tobethereaderspreferredreferencethroughouttheiracademiccareer. Series Editors NeilAshby Professor,ProfessorEmeritus,UniversityofColoradoBoulder,CO,USA WilliamBrantley Professor,FurmanUniversity,Greenville,SC,USA MichaelFowler Professor,UniversityofVirginia,Charlottesville,VA,USA MichaelInglis Professor,SUNYSuffolkCountyCommunityCollege,Selden,NY,USA ElenaSassi Professor,UniversityofNaplesFedericoII,Naples,Italy HelmySherif ProfessorEmeritus,UniversityofAlberta,Edmonton,AB,Canada Teruo Matsushita Electricity and Magnetism New Formulation by Introduction of Superconductivity 123 TeruoMatsushita DepartmentofComputerScience& Electronics KyushuInstituteofTechnology Iizuka,Fukuoka,Japan OriginalJapaneseedition,ShinDenjiki-gaku,ByTeruoMatsushita,Copyright(cid:2)c (2004),Publishedby CORONAPUBLISHINGCO.,LTD.,4-46-10,Sengoku,Bunkyo,Tokyo,Japan ISSN2192-4791 ISSN2192-4805(electronic) ISBN978-4-431-54525-5 ISBN978-4-431-54526-2(eBook) DOI10.1007/978-4-431-54526-2 SpringerTokyoHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013951140 ©SpringerJapan2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Electromagnetism is an important subject in today’s physics. The number of textbooks on electromagnetism is much larger than those on other subjects. This is because abstract concepts are frequently used and therefore it is not easy for students to come to a complete understanding of electromagnetism, although variousphenomenaareconciselydescribedwithmathematics.Forthisreasonmany textbooks have been published to assist students to understand electromagnetism better.Why,then,isanewtextbookonelectromagnetismnecessarynow? Electromagnetismisaclassicalsubjectthatwasalmostcompletelyformulatedin thenineteenthcentury.However,concerningitstheoreticaldescription,thereisstill roomforfurtherprogress.Inaddition,textbooksarerequiredtodescribetheirtopics adequatelywithinalimitedspace.Therefore,thereisalsoroomforimprovementin textbooksfromthetechnicalpointofview. In principle, there is a beautiful formal analogy between static electric and magnetic phenomena,as will be shown in this textbook. However, the analogy is not necessarily perfect in existing textbooks because of the lack of an important concept. Electric materials are classified into conductors and dielectric materials, but only magnets are studied as magnetic materials. While it is known that electricphenomenaindielectricmaterialsandmagneticphenomenainmagnetsare analogoustoeachother,noonehasdiscussedmagneticmaterialsthatcorrespondto electricconductors.However,wehavetonotesuperconductors.Inasuperconductor acurrentflowsonitssurfacetoshieldtheinsideagainstanexternalmagneticfield, sothatthemagneticfluxdensityBiszerointhesuperconductor.Thisisanalogous to the electric phenomenonof a conductorin an externalelectric field. Thatis, an electricchargeappearsonitssurfacetoshieldtheinsideagainstanexternalelectric field,sothattheelectricfieldEiszerointheconductor.Thisisoneoftheremarkable analogiesinthepresentE–Banalogy. Thus, the introduction of the superconductor into electromagnetism, which has not yet been tried systematically, seems to be quite useful for understanding electromagnetism.That is, the analogy between electricity and magnetism can be completedbytheintroductionofthesuperconductor.Therecanbevariouswaysof v vi Preface education without such a comprehensive analogy, and this is another reason why manytextbooksonelectromagnetismhaveappeared. From another point of view, superconductivity is a general phenomenon that appearsinmanysingleelementsandmostmetalliccompounds,ifthecasesofpres- surizationandthinfilms areincluded.The intrinsicpropertyofsuperconductivity, the breaking of Ohm’s law, may seem to be peculiar. However, superconductivity isapurelyphysicalphenomenonthatcanbederivedfromminimizingfreeenergy. In contrast,the empiricalOhm’slaw associated with energydissipationcannotbe derived theoretically, and electromagnetic theory is incomplete for other current- carryingmaterialsinthissense. Usuallystudentslearnaboutstaticmagneticenergyaftertheystudyelectromag- netic induction. One of the appreciable advantages of using a superconductor is the direct derivation of magnetic energy as mechanical work done by magnetic force,similartotheelectricenergyresultingfromtheelectricforce.Thisisbecause themagneticfluxisconservedinasuperconductingcircuitdisconnectedfromany electric sources. As a result, the electromagnetic induction can be predicted for a usualelectriccircuitusingtherelationshipbetweentheenergyandmagneticforce. In electromagnetism the magnetic moment of a magnet caused by spins and orbital motions of electrons is described using a virtual magnetizing current. However, the magnetic moment of a superconductor comes from a real current flowingin it. Hence,the introductionofthe superconductoris alsobeneficialwith regardtopersuasionoftheappropriatenessofthevirtualmagnetizingcurrent. It should be noted that the definition of magnetization is differentfor magnets andsuperconductors.Thatis,magnetizationcomesdirectlyfromthemagnetization M inmagnets,whileitcomesfromthemagneticfieldH insuperconductors.This arises from the difference in the origin of the magnetic moments. According to the definition used for magnets, superconductors are classified as non-magnetic materials. On the other hand, the analogous electric phenomena are electrostatic shielding in conductors and electric polarization in dielectrics. These are similar electricshieldingmechanismscausedbyelectricchargesandpolarizationcharges, but the above-mentioned different terms are used. Such comparison between electricityandmagnetismisalsousefulforeducation. The final merit of the introduction of superconductors is application of the analysismethodofelectromagneticphenomenainsuperconductors.Thecontinuity equation of magnetic flux used for superconductors is useful for estimating the velocity of magnetic flux lines under a magnetic field varying with time. This enablesustounifythemagneticfluxlawandthemotionallawforelectromagnetic induction,whichusuallyhavebeentreatedseparately. The purpose of this textbook is to show the remarkable analogy between static electric phenomena, described in Part I, and static magnetic phenomena, described in Part II. Hence, a comparison between the corresponding chapters in each part, such as Chap. 2 on conductors and Chap. 7 on superconductors, will assistinunderstandingelectromagnetism.Dynamicelectromagneticphenomenaare describedinPartIII. Preface vii IwouldliketoexpressmysincereacknowledgmenttoProf.KlausLuedersatthe BerlinFreeUniversityfortheusefuldiscussionwehad.Inaddition,Iwouldliketo thank Tomoko Onoue, Etsuko Shirahasi, and Kaori Ono for assistance in making electronicfilesanddrawingelectronicfigures. Iizuka,Fukuoka,Japan TeruoMatsushita Contents PartI StaticElectricPhenomena 1 ElectrostaticField .......................................................... 3 1.1 ElectricChargeinVacuum .......................................... 3 1.2 Coulomb’sLaw....................................................... 4 1.3 ElectricField ......................................................... 7 1.4 Gauss’Law........................................................... 11 1.5 ElectricPotential..................................................... 16 1.6 ElectricDipole........................................................ 23 Exercises ..................................................................... 29 2 Conductors.................................................................. 33 2.1 ElectricPropertiesofConductors ................................... 33 2.2 SpecialSolutionMethodforElectrostaticField.................... 41 2.3 ElectrostaticInduction............................................... 46 Exercises ..................................................................... 51 3 ConductorSystemsinVacuum............................................ 55 3.1 CoefficientsinConductorSystem................................... 55 3.2 Capacitor.............................................................. 60 3.3 ElectrostaticEnergy.................................................. 65 3.4 ElectrostaticForce.................................................... 70 Exercises ..................................................................... 73 4 DielectricMaterials......................................................... 75 4.1 ElectricPolarization.................................................. 75 4.2 ElectricFluxDensity................................................. 81 4.3 BoundaryConditions................................................. 85 4.4 ElectrostaticEnergyinDielectricMaterials ........................ 92 Exercises ..................................................................... 95 ix
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