电磁场与电磁波第10讲电流密度电动势电压电流定理-wb

FieldandWaveElectromagnetics电磁场与电磁波2012.3.2311.Poisson’sandLaplace’sEquationsInCartesiancoordinates:Review4.SolutionofElectrostaticProblems23.MethodofImages4.Boundary-ValueProblemsinCartesianCoordinates2.UniquenessofElectrostaticSolutionsuniquenesstheorem:meansthatasolutionofPoisson’sequation(ofwhichLaplace’sequationisaspecialcase)thatsatisfiesthegivenboundaryconditionsisauniquesolution.

Essence:

Theeffectoftheboundary

isreplacedbyoneorseveral

equivalentcharges,andtheoriginalinhomogeneousregionwithaboundarybecomes

aninfinitehomogeneous

space.3MaintopicSteadyElectricCurrents3.EquationofContinuityandKirchhoff’sCurrentLaw1.CurrentDensityandOhm’sLaw2.ElectromotiveForceandKirchhoff’sVoltageLaw41.CurrentDensityandOhm’sLawElectrolyticcurrent(电解电流):aretheresultofmigrationofpositiveandnegativeions;（正离子和负离子徙动的结果）Convectioncurrent(对流电流):resultfrommotionofelectronsand/orionsinavacuumorrarefiedgas;（电子和（或）离子在真空中的运动）Conductioncurrent(传导电流):inconductorsandsemiconductorsarecausedbydriftmotionofconductionelectronsand/orholes;（导体和半导体中的电子和（或）空穴的移动引起的）5TheamountofchargeQpassingthroughtheelementofsurfaceS

withthetimet,isCurrentisthetimerateofchangeofcharge,soConsiderthesteadymotionofonekindofchargecarriers,eachofcharge

q(whichisnegativeforelectrons),acrossanelementofsurfaces

withavelocityu.If

N

isthenumberofchargecarriersperunitvolume,thenintimeteachchargecarriermovesadistanceut

6Definevectorcurrentdensity(电流密度矢量):Itisconvenienttodefineavectorpointfunction,volumecurrentdensity,orsimplycurrentdensity

J,inamperespersquaremeter,ThetotalcurrentI

flowingthroughanarbitrarysurfaceSisthenthefluxoftheJvectorthroughS:Wemayrewrite:whichistherelationbetweentheconvectioncurrentdensityandthevelocityofthechargecarrier.7电流场：大块导体中各点的电流密度矢量J，在不同的点有不同的大小和方向，给定空间每一点处的电流密度矢量J的大小和方向，构成一个矢量场，即：电流场。电流线：电流场由电流线来描述，电流线上每点的切线方向都和该点的电流密度矢量方向一致。电流管：由一束电流线围成的管状区域叫电流管，通过同一个电流管的各个截面的电流强度都相等

电流线：电流场8Inthecaseofconductioncurrentstheremaybemorethanonekindonechargecarriersdriftingwithdifferentvelocities

Itcanbejustifiedanalyticallythatformostconductingmaterialstheaveragedriftvelocityisdirectlyproportionaltotheelectricfieldintensity.FormetallicconductorswewriteWheree

istheelectronmobilityin(m/V·s).WehaveWheree=-Ne

isthechargedensityofthedriftingelectronsandisanegativequantity.

=-ee,isamacroscopicconstitutiveparameterofthemediumcalledconductivity.9---resistance电阻---conductance电导---resistivity电阻率---conductivity电导率parallel：

series：10Theconductivitiesofseveralmediaunitin

S/mMediaConductivitiesMediaConductivitiesSilverSeawaterCopperPurewaterGoldDrysoilAluminumTransformeroilBrassGlassIronRubber11高温超导材料的简介1911年荷兰物理学家发现电阻完全消失的现象仅发生在物质处于极端物理状态的温度-临界温度。1933年，德国科学家发现超导体的抗磁效应。1962年，英国剑桥大学博士研究生证明两个以薄的绝缘层相隔的超导体之间会产生一种特殊现象-隧道效应。1962年，美国Westinghose公司用钛化铌合金拉制成超导电线。（15-25K)1986年，在苏黎世附近一家IBM实验室工作的两位瑞士物理学家宣布，他们研制成含镧和钡的铜酸盐（氧化铜）化合物，其临界温度为30K。更令人惊奇的是此物质为一种陶瓷材料，在常温下具有绝缘体的所用特征。在随之而来的高温超导热中又发现了一批具有较高临界温度的化合物，目前临界温度的最高纪录约是150K（-1230C）12高温超导材料的简介超导材料的基本物理特征：零电阻现象完全抗磁性（迈斯纳效应）超导态并非仅取决于温度(临界电流和临界磁场)普通导体超导体13高温超导材料制备所面临的问题：高温超导材料的制备

材料制造成本高,价格昂贵。

在长距离超导线材的制造上面仍然有很大的难度。（氧化物高温超导陶瓷材料各向异性和短的电子相干长度以及大量晶界的存在严重影响线材的超导电性。）

高温超导材料临界电流和临界磁场的提高仍是科学家研究的难题。-----RobertF.Serverce.Science,295,786(2002).14发展前景节省大量资金缓解环境污染超导电缆、超导发电机、超导电缆预测低电力低能耗灵敏度度高钇钡铜超导薄膜-----应用于谐振器、滤波器、天线等有源器件商品化低电力低能耗钇钡铜超导超导块材-用于磁悬浮、储能飞轮等方面即将实业化预计在2020年左右会形成1500-2000亿美元的超导市场，其中高温超导占一半15Thisequationisaconstitutiverelationoftheconductingmedium.Isotropicmaterialsforwhichthelinearrelationholdsarecalledohmicmedia.Itisgenerallyreferredtoasthe

pointformofOhm’slaw.Itholdsatallpointsinspace.Theunitfor

isamperepervolt-meter(A/V·m),orsiemenspermeter(S/m).Thereciprocalofconductivityiscalledresistivity,

inohm-meter(·m).162.ElectromotiveForceandKirchhoff’sVoltageLawThisequationtellsusthatasteadycurrentcannotbemaintainedinthesamedirectioninaclosedcircuitbyanelectrostaticfield.Asteadycurrentinacircuitistheresultofthemotionofchargecarriers,which,intheirpaths,collidewithatomsanddissipateenergyinthecircuit.Thisenergymustcomefromanon-conservativefield,Theseelectricalenergysources,whenconnectedinanelectriccircuit,provideadrivingforceforthechargecarriers.ThisforcemanifestsitselfasanequivalentimpressedelectricfieldintensityEi.17Chemicalactioncreatesacumulationofpositiveandnegativechargesatelectrodes1and2,respectively.ThesechargesgiverisetoanelectrostaticfieldintensityEbothoutsideandinsidethebattery.Insidethebattery,EmustbeequalinmagnitudeandoppositeindirectiontothenonconservativeEi

producedbychemicalaction,sincenocurrentflowsintheopen-circuitedbatteryandthenetforceactingonthechargecarriersmustvanish.EConductingmediumPNEImpressedsourceEi18Theelectromotiveforceisameasureofthestrengthofthenonconservativesource,denotedby,wehaveOutsidethesourceInsidethesourceOutsidethesourceInsidethesourceWehaveexpressedtheemfofthesourceasalineintegraloftheconservativeEandinterpreteditasavoltagerise.InspiteofthenonconservativenatureofEi,theemfcanbeexpressedasapotentialdifferencebetweenthepositiveandnegativeterminals.EConductingmediumPNEImpressedsourceEi19EConductingmediumPNEImpressedsourceEiIftherearemorethanonesourceofelectromotiveforceandmorethanoneresistor(includingtheinternalresistancesofthesources)intheclosedpath,wegeneralizeEquationisanexpressionofKirchhoff’svoltagelaw.Itstatesthataroundaclosedpathinanelectriccircuitthealgebraicsumoftheemf’s(voltagerises)isequaltothealgebraicsumofthevoltagedropsacrosstheresistances.203.EquationofContinuityandKirchhoff’sCurrentLawTheprinciple(law)ofconservationofcharge:Electricchargesmaynotbecreatednordestroyed,butmerelytransported;allchargeseitheratrestorinmotionmustbeconservedforatalltime；anychangeofchargeinaregionmustbeaccompaniedbyaflowofchargeacrossthesurfaceboundingtheregion.SVI21SincetheequationmustholdregardlessofthechoiceofV,theintegrandsmustbeequal.ThuswehaveThispointrelationshipderivedfromtheprincipleofconservationofchargeiscalledtheequationofcontinuity.Forthesteadycurrents,/t=0,theequationofcontinuityis:Kirchhoff’scurrentlaw:thealgebraicsumofallthecurrentsoutofajunctioninanelectriccircuitiszero.22Wearenowinapositiontoprovethisstatementandtocalculatethetimeittakestoreachanequilibrium.where0istheinitialchargedensityatt=0.Thetimeconstanttiscalledth