E11麦克斯韦方程组

Chapter11DisplacementcurrentMaxwell’sequations§1Maxwell’selectromagnetictheory§2Maxwell’sequations§3Electromagneticwave§4Examples经典电磁理论的奠基人,气体动理论创始人之一.提出了有旋场和位移电流的概念,建立了经典电磁理论,并预言了以光速传播的电磁波的存在.在气体动理论方面,提出了气体分子按速率分布的统计规律.麦克斯韦（1831－1879）英国物理学家1865年麦克斯韦在总结前人工作的基础上，提出完整的电磁场理论，他的主要贡献是提出了“有旋电场”和“位移电流”两个假设，从而预言了电磁波的存在，并计算出电磁波的速度（即光速）.001c(真空中)§1Maxwell’selectromagnetictheory1Maxwell’sfirstsupposition-curlelectricfieldFaraday:iiItddΦiiIEt涡ddΦtlEmLiidddΦSdtB)2()1(EEE.,:)2(无源场涡旋电场EThetotalfieldatapointinspace:;,:)1(有源场静电场EMaxwell：ElectrostaticfieldCurlelectricfieldorinducedelectricfield对电荷有力的作用。同：一个有源、一个无源异：;0d)1(lEElectrostaticfield:lElElEddd)2()1(dtΦStBmddtlEmdddΦ（1）Thedifferencebetweenelectrostaticfieldandinducedelectricfield：实质:Acirculatingelectricfieldcanbecreatedbyachangingmagneticfield.Faraday’slawofelectromagneticinduction.Achangingmagneticfluxcreatesanelectromotiveforce.2Maxwell’ssecondsupposition----displacementcurrent位移电流麦克斯韦对电磁场理论的重大贡献的核心是位移电流的假说，它是将安培环路定理应用于含有电容的交变电路中出现矛盾而引出的。（1）Ampere’scircuitaltheoremConstantcurrent：iIlHdAmpere’slawstatesthatthesameequationholdsiftheplanecircularregionisreplacedbyanysurfacehavingCasitsboundary.通过以环路为周界所有曲面的电流相等，与曲面形状、位置无关。CAmpere’scircuitaltheoremfailsinthecircuitshowninrightFig:在研究含有电容(capacitor)的交变电流电路时，应用安培环路定理就会出现矛盾。1dd1SiSjlHSSurface：20dd2SSjlHSSurface：稳恒情况下得到的安培定理不能用于交变电路中Ontheotherhand,becausenocurrentisemerging,chargeisbuildingupinside,andasaresult,electricfluxisbuildingupbetweenthecapacitorplates,andtherefore,fluxlinespassthroughthehemisphericalsurface.Theelectricfluxisgivenby0/qe（2）ThecorrectionofAmpere’scircuitaltheoremThesuppositionofdisplacementcurrent矛盾是由电流变化造成的，即传导电流在交变电容电路中不再连续；如果假设在变化的电容器中有另一种电流存在，整个电路的电流就又连续了。在电容器中无传导电流但有变化的电场，有电位移。Maxwellarguedthatthisbuildupofelectricfluxcouldbejustwhat’sneededtocorrectAmpere’sequation.Thefluxisrelatedtothecurrentflowingintotheregionbyequation:ttqIdddddd+++++-----ItDddDcjIABcj00DEMaxwellthoughtofthetermasrepresentingakindoffictitiouscurrenttocompletethecircuitthatisinterruptedbythecapacitor.ItiscalledDisplacementcurrentSqSDSS)(20dtqSDtSSddddd)(20Maxwellreasonedthateitherrealcurrent,I,ordisplacementcurrent,Id,(orboth)mightflowanygivensurface,butthesumI+Idthatflowsintoanyregionmustalsoflowout.Totalcurrent：dIII0td/ddttqIddddddTogeneralizeAmpere’scircuitaltheorembyreplacingIbyI+IdIldHSSDtIlHdddd0)2(dd0SStDIlHNote:DisplacementandconductingcurrentsThesame:二者都可产生磁场Thedifference：1位移电流的实质是变化的电场而非电荷的定向移动2位移电流不仅在导体中而且在介质和真空中存在。3位移电流不产生焦耳热。§2Maxwell’sequations)2()1(DDD0d2SDiqSDd1)2()1(BBB0d)1(SB0d)2(SB)2(SdtBdtdldEml)1(diqSD涡静)2()1(EEE涡静)2()1(DDDMeaning:Gauss’slawforelectricity.ComesdirectlyfromCoulomb’slaw.Theelectricfluxoutofaregionisproportionaltothenetchargeinside.Meaning:Faraday’slawofelectromagneticinduction.Achangingmagneticfluxcreatesanelectromotiveforce.TheintegralshapeofMaxwell’sequations)4(SdtDIldHSl传)3(0dSB位传)2()1(HHH位传)2()1(BBBMeaning:Gauss’slawformagnetism.Becausethereerenomagneticmonopoles,thereisneveranynetfluxoutofanyregion.Meaning:Maxwell-Amperelaw.Circuitalmagneticfieldsarecreatedeitherbyelectriccurrentsorbychangingelectricflux.Appendix:(1)Maxwell’sequationsinfreespace:)1(0dSD)2(dtdldEml)3(0dSB)4(SdtDldHSl0eDtBE0BtDjH0(2)Differentialshape(3)MatterequationEDr0HBr0Ej0（4）theboundarycondition电磁场边值条件0)(12EEn012)(jHHn012)(eDDn0)(12BBn:0e:0j当界面两边为介质时：00e00j0)(12DDn0)(12EEn0)(12BBn0)(12HHnFreechargefacialdensityConductingcurrentfacialdensity§3Electromagneticwave1ElectromagneticwaveAchangingmagneticfieldcanproduceanelectricfield.Achangingelectricfieldcanproduceamagneticfield.Wavesarisewhenthesetwoarecombined.ThedynamicEandBcanbecreatedbyeachother.Thisistheessenceoftheelectromagneticwave.变化的电场和变化的磁场相互激发，在空间传播开来，形成电磁波。已发出去的电磁波即使波源消失，波仍将继续存在并向前传播。电磁波是电磁振荡在空间的传播。Electromagneticwavestraveldependingon:(1)Achangingmagneticfieldcanproduceanelectricfield.(2)Achangingelectricfieldcanproduceamagneticfield.正是在这两个基本假说的基础上，麦克斯韦预言了电磁波的存在。2ThecharacteristicsofelectromagneticwavesExampleforelectricdipole：tppcos0任意时刻t空间某点的E、H：Pr）－（＝２０２vvrtrpEcos4sin）－（＝０２vvrtrpHcos4sinThecharacteristicsofelectromagneticwaves(1)ElectricandmagneticfieldoscillationspropagateinphaseE和B都作正弦或余弦的周期性变化，且相位相同(2)EandHareperpendicular,andthebothvectorsareperpendiculartothedirectionofpropagationofwaves电磁波是横波electromagneticwavesaretransversewavesEHSHES(3)TherelationshipofEandH：00HE0000HErr(4)Velocity：rrrrc0011vDEEwe21212(5)Poyntingvector波印亭矢量HBHwm21212222121HEwTheEnergydensityofElectromagneticfieldsEnergyflowdensity能流密度：PoyntingvectorTheenergyperunittime(thepower)acrossaunitarea单位时间内垂直通过传播方向上单