電磁場與電磁波第10講電流密度電動(dòng)勢電壓電流定理-wb

FieldandWaveElectromagnetics電磁場與電磁波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(電解電流):aretheresultofmigrationofpositiveandnegativeions;（正離子和負(fù)離子徙動(dòng)的結(jié)果）Convectioncurrent(對流電流):resultfrommotionofelectronsand/orionsinavacuumorrarefiedgas;（電子和（或）離子在真空中的運(yùn)動(dòng)）Conductioncurrent(傳導(dǎo)電流):inconductorsandsemiconductorsarecausedbydriftmotionofconductionelectronsand/orholes;（導(dǎo)體和半導(dǎo)體中的電子和（或）空穴的移動(dòng)引起的）5TheamountofchargeQpassingthroughtheelementofsurfaceS

withthetimet,isCurrentisthetimerateofchangeofcharge,soConsiderthesteadymotionofonekindofchargecarriers,eachofcharge

q(whichisnegativeforelectrons),acrossanelementofsurfaces

withavelocityu.If

N

isthenumberofchargecarriersperunitvolume,thenintimeteachchargecarriermovesadistanceut

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

J,inamperespersquaremeter,ThetotalcurrentI

flowingthroughanarbitrarysurfaceSisthenthefluxoftheJvectorthroughS:Wemayrewrite:whichistherelationbetweentheconvectioncurrentdensityandthevelocityofthechargecarrier.7電流場：大塊導(dǎo)體中各點(diǎn)的電流密度矢量J，在不同的點(diǎn)有不同的大小和方向，給定空間每一點(diǎn)處的電流密度矢量J的大小和方向，構(gòu)成一個(gè)矢量場，即：電流場。電流線：電流場由電流線來描述，電流線上每點(diǎn)的切線方向都和該點(diǎn)的電流密度矢量方向一致。電流管：由一束電流線圍成的管狀區(qū)域叫電流管，通過同一個(gè)電流管的各個(gè)截面的電流強(qiáng)度都相等

電流線：電流場8Inthecaseofconductioncurrentstheremaybemorethanonekindonechargecarriersdriftingwithdifferentvelocities

Itcanbejustifiedanalyticallythatformostconductingmaterialstheaveragedriftvelocityisdirectlyproportionaltotheelectricfieldintensity.FormetallicconductorswewriteWheree

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

isthechargedensityofthedriftingelectronsandisanegativequantity.

=-ee,isamacroscopicconstitutiveparameterofthemediumcalledconductivity.9---resistance電阻---conductance電導(dǎo)---resistivity電阻率---conductivity電導(dǎo)率parallel：

series：10Theconductivitiesofseveralmediaunitin

S/mMediaConductivitiesMediaConductivitiesSilverSeawaterCopperPurewaterGoldDrysoilAluminumTransformeroilBrassGlassIronRubber11高溫超導(dǎo)材料的簡介1911年荷蘭物理學(xué)家發(fā)現(xiàn)電阻完全消失的現(xiàn)象僅發(fā)生在物質(zhì)處于極端物理狀態(tài)的溫度-臨界溫度。1933年，德國科學(xué)家發(fā)現(xiàn)超導(dǎo)體的抗磁效應(yīng)。1962年，英國劍橋大學(xué)博士研究生證明兩個(gè)以薄的絕緣層相隔的超導(dǎo)體之間會(huì)產(chǎn)生一種特殊現(xiàn)象-隧道效應(yīng)。1962年，美國Westinghose公司用鈦化鈮合金拉制成超導(dǎo)電線。（15-25K)1986年，在蘇黎世附近一家IBM實(shí)驗(yàn)室工作的兩位瑞士物理學(xué)家宣布，他們研制成含鑭和鋇的銅酸鹽（氧化銅）化合物，其臨界溫度為30K。更令人驚奇的是此物質(zhì)為一種陶瓷材料，在常溫下具有絕緣體的所用特征。在隨之而來的高溫超導(dǎo)熱中又發(fā)現(xiàn)了一批具有較高臨界溫度的化合物，目前臨界溫度的最高紀(jì)錄約是150K（-1230C）12高溫超導(dǎo)材料的簡介超導(dǎo)材料的基本物理特征：零電阻現(xiàn)象完全抗磁性（邁斯納效應(yīng)）超導(dǎo)態(tài)并非僅取決于溫度(臨界電流和臨界磁場)普通導(dǎo)體超導(dǎo)體13高溫超導(dǎo)材料制備所面臨的問題：高溫超導(dǎo)材料的制備

材料制造成本高,價(jià)格昂貴。

在長距離超導(dǎo)線材的制造上面仍然有很大的難度。（氧化物高溫超導(dǎo)陶瓷材料各向異性和短的電子相干長度以及大量晶界的存在嚴(yán)重影響線材的超導(dǎo)電性。）

高溫超導(dǎo)材料臨界電流和臨界磁場的提高仍是科學(xué)家研究的難題。-----RobertF.Serverce.Science,295,786(2002).14發(fā)展前景節(jié)省大量資金緩解環(huán)境污染超導(dǎo)電纜、超導(dǎo)發(fā)電機(jī)、超導(dǎo)電纜預(yù)測低電力低能耗靈敏度度高釔鋇銅超導(dǎo)薄膜-----應(yīng)用于諧振器、濾波器、天線等有源器件商品化低電力低能耗釔鋇銅超導(dǎo)超導(dǎo)塊材-用于磁懸浮、儲能飛輪等方面即將實(shí)業(yè)化預(yù)計(jì)在2020年左右會(huì)形成1500-2000億美元的超導(dǎo)市場，其中高溫超導(dǎo)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