北京理工大学电磁场Ch.1课件

电磁场理论（第一讲）

ElectromagneticFieldTheory(Lecture1)盛新庆（ShengXin-Qing）电磁仿真中心（CenterforElectromagneticSimulation）北京理工大学信息科学技术学院（SchoolofInformationScienceandTechnology，BeijingInstituteofTechnology）电子信箱：xsheng@

电话:68949049/daoshi/博导网页/盛新庆.htm1.OutlineABriefIntroductionofThisCourse

Explainthetitle;Importance;Contents;Referencebooks;

ThePhysicalBackgroundofEstablishingElectromagneticWaveTheory2.TitleofThisCourseElectromagneticFieldTheoryElectromagneticWaveTheoryElectricElectricsElectronicsMagneticMagnetismTheory:Astatementorgroupofstatementsestablishedbyreasonedargumentbasedonknownfacts,intendedtoexplainaparticularfactorevent (LongmanDic.)Setofreasonedideasintendedtoexplainfactsorevents(OxfordDic.)人们由实践概括出来的关于自然界和社会的知识的有系统的结论（现代汉语词典）3.

ImportanceofThisCourseOneofFundamentalCoursesinOurInformationAge

WirelessCommunications(SatellitecommunicationMobilePhone),Radar,etal.stealthyaircraft,low-observabletargetsOneofMasterworksinthewholemankindcivilizationhistory4.

ContentofThisCourseHowisElectromagneticFieldTheoryestablished?(Ch.1)PhysicalBackground,MathematicalBackground,AcademicTraditionBackgroundHowtoemployElectromagneticFieldTheorytosolvethetypicalproblemsinthecurrentinformationAge?PropagationandTransmission,Radiation,Scattering(Ch.2,Ch.3,Ch.4)5.ReferenceBooksofThisCourse《电磁波述论》，盛新庆，科学出版社《Field

andWaveElectromagnetics》，David

K.Cheng,清华大学出版社ExerciseProblems：6.RequirementofThisCourseYouarerequiredtodoexercisesandexaminationsinEnglish.7.PhysicalBackgroundofEstablishingElectromagneticWaveTheoryKnowledgeinElectricsandMagntism

BeforeCoulomb’sLaw AfterCoulomb’sLaw8.BeforeCoulomb’sLawEastern

100BC-100A.D.

triboelectricity,triboluminescence

500BCmagneticstone1000A.D.Compass,magneticdeclinationangle

1600A.D. ElectricinLigntningWestern600BCamber1492A.D.magneticdeclinationangle

Observation9.Coulomb’sLawCoulomb,French,1736-18061784-1785Torsionbalance1772Cavendish

1785Coulomb

1872Maxwell

1971Williamsetal.

permittivity10.Ampere’sLawOersted,1777-1851,Denmark1820MagnetizedneedleBiot-Savart-LaplaceAmpere’sLawpermeability11.Faraday’sLaw1,VaringElectricCurrent2,VaringMagneticField……Faraday,1791-1867,Britain1831Neumann,1798-1895,GermanyElectromotiveforce12.MathematicalBackgroundofEstablishingElectromagneticWaveTheoryCalculusNewton,1642-1727,BritianLeibnitz,1646-1716,GermanyVectorAnalysis

Hamilton,1805-1865,BritainGibbs,1839-1903,U.S.AHeaviside,1850-1925,Britain

13.VectorAnalysis

DefinitionofVectorVectorRepresentationTransformationsofVectorRepresentationinDifferentCoordinateSystems

14.VectorRepresentationxyzzxyz15.TransformationsofVectorRepresentationinDifferentCoordinateSystems

xyzz16.VectorAddition

and

Substration

？17.DotMultiplicationofVectorsABCommutativeDistributive18.CrossMultiplicationofVectorsABanticommutative19.VectorIdentities20.VectorAnalysis

OperatorsGradientDivergenceCurl

21.GradientofaScalarFieldCartesianCoordinatesCylindricalCoordinatesSphericalCoordinatesThegradientoperatorusuallyoperatesonascalarphysicalquantity,andtheresultoftheoperationisavectorwhosemagnitudeequalstothemaximumrateofchangeofthephysicalquantityperunitdistanceandwhosedirectionisalongthedirectionofmaximumincrease.

22.VectorIdentities23.DivergenceofaVectorField

CartesianCoordinatesCylindricalCoordinatesSphericalCoordinatesDefinitionGaussTheoremNetoutwardfluxofFperunitvolumeasthevolumeaboutthepointtendstozero.24.Example If ,

find(ordivA)at thepoint(1,-1,1).Atpoint(1,-1,1)25.CurlofaVectorField

CartesianCoordinatesCylindricalCoordinatesSphericalCoordinatesDefinitionStokes’sTheoremNetcirculationfluxofFperunitareaastheareaaboutthepointtendstozeroDirectionisthenormaldirectionofthearea26.Example If ,

find

(orcurlA)atthepoint(1,-1,1).Atpoint(1,-1,1)27.Often-UsedSymbols28.VectorIdentities If ,wecandefineVectorcanexpressedasthegradientofascalarfieldIf ,wecandefineVectorcanexpressedasthecurlofanothervectorfiled.29.VectorIdentities30.VectorTheorems

First-KindScalarGreenTheoremSecond-KindScalarGreenTheoremFirst-KindVectorGreenTheoremSecond-KindVectorGreenTheorem31.Helmholtz’sTheorem

Avectorfieldisdeterminedtowithinanadditiveconstantifbothitsdivergenceanditscurlarespecifiedeverywhere.32.WesternAcademicTradition西方科学的发展是以两个伟大的成就为基础，那就是：希腊哲学家发明的形式逻辑体系（在欧几里得几何学中），以及通过系统的实验发现有可能找出因果关系（在文艺复兴时期）。

----《爱因斯坦文集》第一卷第574页

33.DevelopmentofWesternAcademicTraditionEuclid（欧几里得）

《Euclid’sElements》

《几何原本》I.Newton

（牛顿）《MathematicalPrincipleofNaturalPhilosophy》

《自然哲学的数学原理》I.Kant

（康德）

《CritiqueofPureReason》

《纯粹理性的批判》34.欧几里得的《几何原本》《Euclid’sElements》Euclid（300BC）EducatedinPlato

Academy

(柏拉图学院)，livedinAlexanderCity(亚历山大城)《Euclid’sElements》Beginwithdefinitionsandaxioms，thenprove467propositionsbyreason,include13Chs.，35.牛顿的《自然哲学的数学原理》

《MathematicalPrincipleofNaturalPhilosophy》Newton（1642-1727）EducatedinTrinityCollegeofCambridgeUniv.(剑桥的三一学院)，livedinLincolnshire、Cambridge、London

《MathematicalPrincipleofNaturalPhilosophy

》ThreeVersions(1687,1713,1726,拉丁文;1729,英文)MechanicsTheory(ThreeMechanicsLawsandUniversalGravitation’sLaw,reasoned,explainmanynaturalfacts,moreimportantly,accuratelypredictednaturalphenomena)36.康德的《纯粹理性的批判》

Kant’s《CritiqueofPureReason》Kant（1724-1804）受教于哥尼斯堡大学，生活于哥尼斯堡《CritiqueofPureReason》TwoVersions（1781，1787）PureinvestigationonacademictraditionfoundedbyNewtonFourFamousAntinomies37.ChineseAcademicTradition“博学而笃志，切问而近思，仁在其中矣。”Widelylearningandsincerelyintend,questionpreciselyandreflectwhatisathand,‘ren’willbethere----《论语(theAnalectsofConfucius)

》子张篇第十九Whatkindofquestionsareworthtobestudied?QuestionscloselyrelativetoourlifeHowtostudy?WidelylearningandSincerelyIntend38.DevelopmentofChineseAcademicTradition孔子（Confucius）

《论语

(

theAnalectsofConfucius)

》刘徽（Liu-Hui）

《九章算术注》《NineChaptersontheMathematicalArts》沈括（Shen-Kuo）

《梦溪笔谈》39.《论语（TheAnalectsofConfucius）

》

Confucius（551BC.9.28-479BC）生于今山东曲阜，曾跟鲁太师习周礼《论语

(TheAnalectsofConfucius)

》

陈述也采取一问一答式。共有20篇，约11000余字40.刘徽的《九章算术注》

刘徽（公元260年左右，魏晋时期）

LivedinShandongProvince,ZhoupingCounty(生于今山东省邹平县)《九章算术注》（263年）《NineChaptersontheMathematicalArts》Contents:Ninemathematicalproblemsconcernedpeople’slife.Style:Firstlistproblemsandvariants,thengivethesolutionprocedure.Chaptershavenologicalrelationsandnospecialorder.41.

沈括的《梦溪笔谈》沈括（公元1033-1097，北宋）

杭州钱塘县人，曾跟鲁太师习周礼《梦溪笔谈》

以笔记的体裁，记录、稽考、订正了大量的当时和前代的典章制度、掌故逸事、文物考古、自然知识等。共609条，其中科技条目约255条，占42%，涉及自然观、乐律、数学、物理、天文、气象、地理建筑、水利等。42.ComparisonofWesternandChineseAcademicTraditionChineseAcademicTradition重记录、重“述而不作(narrate,notinvent)”（《论语》述而篇第七），重“学而时习之(practise)”（《论语》学而篇第一），在反复的咏颂中，以达“其义自见”（《艺文类聚》卷五十五），“熟能生巧”（《归田录·卖油翁》），“温故而知新”（《论语》为政篇第二）对材料的整理所下功夫是较少的。这里的“整理”指的是从材料中提炼出观念，并用观念来统领解释材料。

43.DisadvantagesofWesternAcademicTradition更不妨回顾一下思想史罢。许多严密周全的思想和哲学系统经不起时间的推排销蚀，在整体上都垮塌了，但是它们的一些个别见解还为后世所采取而未失去时效。……往往整个理论系统剩下来的有价值东西只是一些片段思想。脱离了系统而遗留的片段思想和萌发而未构成系统的片断思想，两者同样是零碎的。眼里只有长篇大论，瞧不起片言只语，甚至陶醉于数量，重视废话一吨，轻视微言一克，那是浅薄庸俗的看法——假使不是懒惰粗浮的借口。

----钱钟书，《七缀集》，第33-34页44.AdavantagesofofWesternAcademicTraditionThetraditionmakesthematerialsclearandconcise.Moreimportantly,itusuallycanabstractoriginalideasfrommaterials,andgivepeoplestrongfaith,bringimaginationandcretivity.StrongPower,Imagination,Creativity45.ComparisonofWesternandChineseAcademicTraditionWesternacademictraditionemphasizesabstractingconcepts,constructinglogicalsystems,andinventingthefuturewithstrongfaith.(

西学传统以提炼观念，构建逻辑体系，进而以坚定的信念创造未来为基本特征，其长在于条理清晰，创造性极强；其短在于创造的观念往往远离人类生活，容易形而上，华而不实，以偏代全，误入歧途，走向极端。)Chineseacademictraditionemphasizeswidelylearning,practiceagainandagain.(

华夏传统以博采、敏感、反复、熟练、温故而知新，以达赏玩游乐之境界为基本精神，其长在于不离人类健康生活的轨道，保证中庸而行；其短也很明显，在于创造性较弱。)46.AbstractionfromCoulomb’sLawElectricFieldIntensityandElectricFluxDensityCoulomb’sLaw47.AbstractionfromAmpere’sLawMagneticFieldIntensityandMagneticFluxDensityAmpere’sLaw48.AbstractionfromFaraday’sLawFaraday’sLaw49.Maxwell’sContributionFaraday’sLawAmpere’sLawCoulomb’sLawCoulomb’sLawAmpere’sLawMaxwell’sDisplacementCurrentDensityAmpere’sLawAmpere-Maxwell’sLaw50.ExampleConductioncurrentdareaADisplacementcurrent51.ElectromagneticFieldTheory

-----Maxwell’sEquationAmpere’sLawCoulomb’sLaw52.PredictionofElectromagneticWaveAmpere’sLawCoulomb’sLawFizeaumeasuredthelightspeedin184953.ElectromagneticFieldTheory

-----Maxwell’sEquationAmpere’sLawCoulomb’sLawDifferentialFormIntegralForm54.PredictionofElectromagneticWaveAmpere’sLawCoulomb’sLawFizeaumeasuredthelightspeedin184955.Hertz’sExperimentsHertzdidanexperimentin1888toverifytheexistenceofelectromagneticwave56.Maxwell’sequationspredicttheexistenceofelectromagneticwaves.Theyimposenolimitonthefrequencyofthewaves.AllEMwavesinwhateverfrequencyrangepropagateinamediumwiththesamevelocityMicrowavefrequencyrangeLband 1-2GHzS

band 2-4GHzCband 4-8GHzXband 8-12GHzKuband 12.4-18GHzK

band 18-26.35GHzKa

band 26.5-40GHzElectromagneticspectrum57.LightfrequencyrangeRed0.72mViolet0.38mWavelength:Frequency:MF200-3000kHzAM,maritimeHF3MHz-30MHzSWradioVHF30-300MHzTV,FM,policeUHF300-3000MHzRadar,TVSHF3-30GHzRadar,satellitecommunicationElectromagneticspectrum58.DeterminedFormulationofElectromagneticProblemsMaxwell’sEquationsConstitutiveRelationsBoundaryConditions59.ConstitutiveRelations

60.Relativepermittivityofmaterials(

r)

Vacuum

QuartzAir

SeawaterWood(dry)

DistilledwaterDrySoil

PetroleumoilGlass

61.Conductivitiesofmaterials()

silver ironcopper seawatergold distilledwateraluminum transformeroilbrass 62.BoundaryConditionsForprobleminvolvingcontiguousregionsofdifferent&,weneedtoknowtheboundaryconditions:FromtheintegralformsofMaxwell’sequations,wegetFortangentialcomponents,Fornormalcomponentsmedium1medium263.FromMaxwell’sequations:(1)Faraday’sLawWhenwtendsto0,E1t=E2tTangentialE-fieldiscontinuousacrossaninterfaceE1E2E3E4wlmedium1medium2yxz64.FromMaxwell’sequations:(2)Ampere’sLawWhenwtendsto0,JzwJs,Ht2–Ht1=JsTangentialH-fieldisdiscontinuousacrossaninterfacewhereafreesurfacecurrentexistsH1H2H3H4wlmedium1medium2yxz65.FromMaxwell’sequations:(3)Gauss’sLawNormalcomponentofDfieldisdiscontinuousacrossaninterfacewhereasurfacechargeexists.TheamountofdiscontinuitybeingequaltothesurfacechargedensityD1D2medium1medium266.FromMaxwell’sequations:(4)NormalcomponentofBfieldiscontinuousacrossaninterfaceB1B2medium1medium267.Interfacebetween2losslesslinearmedia NofreechargesandnosurfacecurrentsatinterfacebetweentwolosslessmediaInterfacebetweenadielectricandaperfectconductorSpecialCases68.Insolvingfieldproblems,goodconductorsareoftenconsideredasperfectconductorsinregardtoboundaryconditions.*Thechargescanonlyresideonthesurface.Conductivitiesofmaterials()

silver,copper,gold,aluminum,brass,iron

Interiorofaperfectconductor,E

=

0(otherwiseJ=E).

Therefore,D=0Interrelationshipbetween(E,D)and(B,H)fromMaxwell’s,B=H=0Interfacebetweenadielectricandaperfectconductor69.Medium1 Medium2122perfect1dielectricconductor12++++++++++Interfacebetweenadielectricandaperfectconductor70.DeterminedFormulationof

ElectromagneticProblemsMaxwell’sEquationsConstitutiveRelationsBoundaryConditions71.ElectrostaticProblemsElectromagneticfieldisinvariantwithtimeBoundaryconditions72.ImageMethodChargeQ(x1,y1,0)xyCharge-Q(x1,-y1,0)ChargeQ(x1,y1,0)xyPerfectlyConductingplaneP(X,Y,Z)73.CapacitanceQ-QVAdE74.MagnetostaticProblemsElectromagneticfieldisinvariantwithtimeBoundaryconditions75.InductanceAninductoristhemagneticanalogueofanelectriccapacitor.76.StaticElectromagneticProblemsElectrostaticProblemsMagnetostaticProblems77.Inengineering,sinusoidaltimefunctionsareeasytogenerate;arbitraryperiodictimefunctionscanbeexpandedintoFourierseriesofharmonicsinusoidalc