電磁場與電磁波第10講電流密度電動勢電壓電流定理-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;（正離子和負離子徙動的結果）Convectioncurrent(對流電流):resultfrommotionofelectronsand/orionsinavacuumorrarefiedgas;（電子和（或）離子在真空中的運動）Conductioncurrent(傳導電流):inconductorsandsemiconductorsarecausedbydriftmotionofconductionelectronsand/orholes;（導體和半導體中的電子和（或）空穴的移動引起的）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：大塊導體中各點的電流密度矢量J，在不同的點有不同的大小和方向，給定空間每一點處的電流密度矢量J的大小和方向，構成一個矢量場，即：電流場。電流線：電流場由電流線來描述，電流線上每點的切線方向都和該點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，通過同一個電流管的各個截面的電流強度都相等

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---resistivity電阻率---conductivity電導率parallel：

series：10Theconductivitiesofseveralmediaunitin

S/mMediaConductivitiesMediaConductivitiesSilverSeawaterCopperPurewaterGoldDrysoilAluminumTransformeroilBrassGlassIronRubber11高溫超導材料的簡介1911年荷蘭物理學家發(fā)現電阻完全消失的現象僅發(fā)生在物質處于極端物理狀態(tài)的溫度-臨界溫度。1933年，德國科學家發(fā)現超導體的抗磁效應。1962年，英國劍橋大學博士研究生證明兩個以薄的絕緣層相隔的超導體之間會產生一種特殊現象-隧道效應。1962年，美國Westinghose公司用鈦化鈮合金拉制成超導電線。（15-25K)1986年，在蘇黎世附近一家IBM實驗室工作的兩位瑞士物理學家宣布，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熱中又發(fā)現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錄約是150K（-1230C）12高溫超導材料的簡介超導材料的基本物理特征：零電阻現象完全抗磁性（邁斯納效應）超導態(tài)并非僅取決于溫度(臨界電流和臨界磁場)普通導體超導體13高溫超導材料制備所面臨的問題：高溫超導材料的制備

材料制造成本高,價格昂貴。

在長距離超導線材的制造上面仍然有很大的難度。（氧化物高溫超導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重影響線材的超導電性。）

高溫超導材料臨界電流和臨界磁場的提高仍是科學家研究的難題。-----RobertF.Serverce.Science,295,786(2002).14發(fā)展前景節(jié)省大量資金緩解環(huán)境污染超導電纜、超導發(fā)電機、超導電纜預測低電力低能耗靈敏度度高釔鋇銅超導薄膜-----應用于諧振器、濾波器、天線等有源器件商品化低電力低能耗釔鋇銅超導超導塊材-用于磁懸浮、儲能飛輪等方面即將實業(yè)化預計在2020年左右會形成1500-2000億美元的超導市場，其中高溫超導占一半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