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首页 电磁场理论

电磁场理论.pdf

电磁场理论

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“main”page����ELECTROMAGNETICFIELDTHEORYΥBoThidéUPSILONMEDIA“main”page����“main”page����BoThidéELECTROMAGNETICFIELDTHEORY“main”page����AlsoavailableELECTROMAGNETICFIELDTHEORYEXERCISESbyTobiaCarozzi,AndersEriksson,BengtLundborg,BoThidéandMattiasWaldenvik“main”page����ELECTROMAGNETICFIELDTHEORYBoThidéSwedishInstituteofSpacePhysicsandDepartmentofAstronomyandSpacePhysicsUppsalaUniversity,SwedenΥUPSILONMEDIA·UPPSALA·SWEDEN“main”page����ThisbookwastypesetinLATEXεonanHPseriesworkstationandprintedonanHPLaserJetGNprinterCopyright©,,andbyBoThidéUppsala,SwedenAllrightsreservedElectromagneticFieldTheoryISBNXXXXXXXXXX“main”pagei����ContentsPrefacexiClassicalElectrodynamicsElectrostaticsCoulomb’slawTheelectrostaticfieldMagnetostaticsAmpère’slawThemagnetostaticfieldElectrodynamicsEquationofcontinuityMaxwell’sdisplacementcurrentElectromotiveforceFaraday’slawofinductionMaxwell’smicroscopicequationsMaxwell’smacroscopicequationsElectromagneticDualityExampleDualityoftheelectromagnetodynamicequationsExampleMaxwellfromDiracMaxwellequationsforafixedmixingangleExampleThecomplexfieldsixvectorExampleDualityexpressedinthecomplexfieldsixvectorBibliographyElectromagneticWavesThewaveequationThewaveequationforEThewaveequationforBThetimeindependentwaveequationforEPlanewavesTelegrapher’sequationi“main”pageii����iiCONTENTSWavesinconductivemediaObservablesandaveragesBibliographyElectromagneticPotentialsTheelectrostaticscalarpotentialThemagnetostaticvectorpotentialTheelectromagneticscalarandvectorpotentialsElectromagneticgaugesLorentzequationsfortheelectromagneticpotentialsGaugetransformationsSolutionoftheLorentzequationsfortheelectromagneticpotentialsTheretardedpotentialsBibliographyTheElectromagneticFieldsThemagneticfieldTheelectricfieldBibliographyRelativisticElectrodynamicsThespecialtheoryofrelativityTheLorentztransformationLorentzspaceMetrictensorRadiusfourvectorincontravariantandcovariantformScalarproductandnormInvariantlineelementandpropertimeFourvectorfieldsTheLorentztransformationmatrixTheLorentzgroupMinkowskispaceCovariantclassicalmechanicsCovariantclassicalelectrodynamicsThefourpotentialTheLiénardWiechertpotentialsTheelectromagneticfieldtensorBibliographyDownloadedfromhttp:wwwplasmauuseCEDBookDraftversionreleasedthNovemberat:“main”pageiii����iiiInteractionsofFieldsandParticlesChargedParticlesinanElectromagneticFieldCovariantequationsofmotionLagrangeformalismHamiltonianformalismCovariantFieldTheoryLagrangeHamiltonformalismforfieldsandinteractionsTheelectromagneticfieldExampleFieldenergydifferenceexpressedinthefieldtensorOtherfieldsBibliographyInteractionsofFieldsandMatterElectricpolarisationandtheelectricdisplacementvectorElectricmultipolemomentsMagnetisationandthemagnetisingfieldEnergyandmomentumTheenergytheoreminMaxwell’stheoryThemomentumtheoreminMaxwell’stheoryBibliographyElectromagneticRadiationTheradiationfieldsRadiatedenergyMonochromaticsignalsFinitebandwidthsignalsRadiationfromextendedsourcesLinearantennaMultipoleradiationTheHertzpotentialElectricdipoleradiationMagneticdipoleradiationElectricquadrupoleradiationRadiationfromalocalisedchargeinarbitrarymotionTheLiénardWiechertpotentialsRadiationfromanacceleratedpointchargeExampleThefieldsfromauniformlymovingchargeExampleTheconvectionpotentialandtheconvectionforceDraftversionreleasedthNovemberat:Downloadedfromhttp:wwwplasmauuseCEDBook“main”pageiv����ivCONTENTSRadiationforsmallvelocitiesBremsstrahlungExampleBremsstrahlungforlowspeedsandshortaccelerationtimesCyclotronandsynchrotronradiationCyclotronradiationSynchrotronradiationRadiationinthegeneralcaseVirtualphotonsRadiationfromchargesmovinginmatterVavilovˇCerenkovradiationBibliographyFFormulaeFTheElectromagneticFieldFMaxwell’sequationsConstitutiverelationsFFieldsandpotentialsVectorandscalarpotentialsLorentz’gaugeconditioninvacuumFForceandenergyPoynting’svectorMaxwell’sstresstensorFElectromagneticRadiationFRelationshipbetweenthefieldvectorsinaplanewaveFThefarfieldsfromanextendedsourcedistributionFThefarfieldsfromanelectricdipoleFThefarfieldsfromamagneticdipoleFThefarfieldsfromanelectricquadrupoleFThefieldsfromapointchargeinarbitrarymotionFThefieldsfromapointchargeinuniformmotionFSpecialRelativityFMetrictensorFCovariantandcontravariantfourvectorsFLorentztransformationofafourvectorFInvariantlineelementFFourvelocityFFourmomentumFFourcurrentdensityFFourpotentialDownloadedfromhttp:wwwplasmauuseCEDBookDraftversionreleasedthNovemberat:“main”pagev����vFFieldtensorFVectorRelationsFSphericalpolarcoordinatesBasevectorsDirectedlineelementSolidangleelementDirectedareaelementVolumeelementFVectorformulaeGeneralrelationsSpecialrelationsIntegralrelationsBibliographyAppendicesMMathematicalMethodsMScalars,VectorsandTensorsMVectorsRadiusvectorMFieldsScalarfieldsVectorfieldsTensorfieldsExampleMTensorsinDspaceMVectoralgebraScalarproductExampleMInnerproductsincomplexvectorspaceExampleMScalarproduct,normandmetricinLorentzspaceExampleMMetricingeneralrelativityDyadicproductVectorproductMVectoranalysisThedeloperatorExampleMThefourdeloperatorinLorentzspaceThegradientExampleMGradientsofscalarfunctionsofrelativedistancesinDThedivergenceDraftversionreleasedthNovemberat:Downloadedfromhttp:wwwplasmauuseCEDBook“main”pagevi����viCONTENTSExampleMDivergenceinDTheLaplacianExampleMTheLaplacianandtheDiracdeltaThecurlExampleMThecurlofagradientExampleMThedivergenceofacurlMAnalyticalMechanicsMLagrange’sequationsMHamilton’sequationsBibliographyDownloadedfromhttp:wwwplasmauuseCEDBookDraftversionreleasedthNovemberat:“main”pagevii����ListofFiguresCoulombinteractionAmpèreinteractionMovingloopinavaryingBfieldRelativemotionoftwoinertialsystemsRotationinaDEuclideanspaceMinkowskidiagramLinearonedimensionalmasschainRadiationinthefarzoneRadiationfromamovingchargeinvacuumAnacceleratedchargeinvacuumAngulardistributionofradiationduringbremsstrahlungLocationofradiationduringbremsstrahlungRadiationfromachargeincircularmotionSynchrotronradiationlobewidthTheperpendicularfieldofamovingchargeVavilovˇCerenkovconeMSurfaceelementofamaterialbodyMTetrahedronlikevolumeelementofmattervii“main”pageviii����“main”pageix����TothememoryofLEVMIKHAILOVICHERUKHIMOVdearfriend,remarkablephysicistandatrulygreathuman“main”pagex����“main”pagexi����PrefaceThisbookistheresultofatwentyfiveyearlongloveaffairIn,ItookmyfirstadvancedcourseinelectrodynamicsattheTheoreticalPhysicsdepartment,UppsalaUniversityShortlythereafter,Ijoinedtheresearchgroupthereandtookonthetaskofhelpingmysupervisor,professorPEROLOFFRÖMAN,withthepreparationofanewversionofhislecturenotesonElectricityTheoryThesetwothingsopenedupmyeyesforthebeautyandintricacyofelectrodynamics,alreadyattheclassicallevel,andIfellinlovewithitEversincethattime,Ihaveoffandonhadreasontoreturntoelectrodynamics,bothinmystudies,researchandteaching,andthecurrentbookistheresultofmyownteachingofacourseinadvancedelectrodynamicsatUppsalaUniversitysometwentyoddyearsafterIexperiencedthefirstencounterwiththissubjectThebookistheoutgrowthofthelecturenotesthatIpreparedforthefourcreditcourseElectrodynamicsthatwasintroducedintheUppsalaUniversitycurriculumin,tobecomethefivecreditcourseClassicalElectrodynamicsinTosomeextent,partsofthesenoteswerebasedonlecturenotesprepared,inSwedish,byBENGTLUNDBORGwhocreated,developedandtaughttheearlier,twocreditcourseElectromagneticRadiationatourfacultyIntendedprimarilyasatextbookforphysicsstudentsattheadvancedundergraduateorbeginninggraduatelevel,IhopethebookmaybeusefulforresearchworkerstooItprovidesathoroughtreatmentofthetheoryofelectrodynamics,mainlyfromaclassicalfieldtheoreticalpointofview,andincludessuchthingsaselectrostaticsandmagnetostaticsandtheirunificationintoelectrodynamics,theelectromagneticpotentials,gaugetransformations,covariantformulationofclassicalelectrodynamics,force,momentumandenergyoftheelectromagneticfield,radiationandscatteringphenomena,electromagneticwavesandtheirpropagationinvacuumandinmedia,andcovariantLagrangianHamiltonianfieldtheoreticalmethodsforelectromagneticfields,particlesandinteractionsTheaimhasbeentowriteabookthatcanservebothasanadvancedtextinClassicalElectrodynamicsandasapreparationforstudiesinQuantumElectrodynamicsandrelatedsubjectsInanattempttoencourageparticipationbyotherscientistsandstudentsinxi“main”pagexii����xiiPREFACEtheauthoringofthisbook,andtoensureitsqualityandscopetomakeitusefulinhigheruniversityeducationanywhereintheworld,itwasproducedwithinaWorldWideWeb(WWW)projectThisturnedouttobearathersuccessfulmoveBymakinganelectronicversionofthebookfreelydownloadableonthenet,IhavenotonlyreceivedcommentsonitfromfellowInternetphysicistsaroundtheworld,butknow,fromWWW‘hit’statisticsthatatthetimeofwritingthis,thebookservesasafrequentlyusedInternetresourceThiswayitismyhopethatitwillbeparticularlyusefulforstudentsandresearchersworkingunderfinancialorothercircumstancesthatmakeitdifficulttoprocureaprintedcopyofthebookIamgratefulnotonlytoPerOlofFrömanandBengtLundborgforprovidingtheinspirationformywritingthisbook,butalsotoCHRISTERWAHLBERGatUppsalaUniversityforinterestingdiscussionsonelectrodynamicsingeneralandonthisbookinparticular,andtomyformergraduatestudentsMATTIASWALDENVIKandTOBIACAROZZIaswellasANDERSERIKSSON,allattheSwedishInstituteofSpacePhysics,UppsalaDivision,andwhohaveparticipatedintheteachingandcommentedonthematerialcoveredinthecourseandinthisbookThanksarealsoduetomylongtermspacephysicscolleagueHELMUTKOPKAoftheMaxPlanckInstitutfürAeronomie,Lindau,Germany,whonotonlytaughtmeaboutthepracticalaspectsoftheofhighpowerradiowavetransmittersandtransmissionlines,butalsoaboutthemoredelicateaspectsoftypesettingabookinTEXandLATEXIamparticularlyindebtedtoAcademicianprofessorVITALIYLGINZBURGforhismanyfascinatingandveryelucidatinglectures,commentsandhistoricalfootnotesonelectromagneticradiationwhilecruisingontheVolgariverduringourjointRussianSwedishsummerschoolsFinally,IwouldliketothankallstudentsandInternetuserswhohavedownloadedandcommentedonthebookduringitslifeontheWorldWideWebIdedicatethisbooktomysonMATTIAS,mydaughterKAROLINA,myhighschoolphysicsteacher,STAFFANRÖSBY,andtomyfellowmembersoftheCAPELLAP

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