E6导体与电介质课件

§1ConductorsintheElectrostaticField§2DielectricsandPolarization

intheElectricField§3CapacitanceandCapacitor§4TheEnergyofElectricfield

Chapter6ConductorsandDielectricsintheElectrostaticField§5Application1Electrostaticinduction§1ConductorsintheElectrostaticField+++++++++感应电荷+2ElectrostaticEquilibriumInelectrostaticequilibrium,allthefreeelectronareatrest.达到静电平衡时，所有自由电子都处于静止状态。++++++++Proving1Notangentialcomponentcanexist。导体表面附近电场强度垂直于等势面。Proving2++++++++++++3DistributionofChargea)AllofthechargesisonthesurfaceoftheconductorProve：b)TheelectricfieldonthesurfaceofaconductorsNote:Thefieldatthesurfaceoftheconductor(andjustoutside)c)DistributionofChargeofSphericalConductorRestrictingfactors：theelectricfieldiszeroinsideaconductor.E=0Conductorshell（腔）(1)NochargeinaconductorshellaTheelectricfieldiszeroinsideinsideconductorandshell导体内、空腔内场强皆为零；bTheconductorandshellareequipotential

导体、空腔为等势体；cThechargemustlieonthesurface

内表面处处没有电荷，电荷只分布在外表面.(2)AchargeqinaconductorshellOntheinnersurfaceoftheshellthechargeis

-q.Ontheoutersurfaceoftheshellthechargeisq.ItisdeterminedbyGauss’slaw.两球半径分别为R1、R2，带电量q1、q2，设两球相距很远，当用导线将彼此连接时，电荷将如何分布？解用导线连接后，两球带电量之和守恒R2R1如果两球相距较近，结果怎样？例2思考已知导体球壳A带电量为Q，导体球B带电量为q

(1)将A接地后再断开，电荷和电势的分布；解A与地断开后,ArR1R2B-q电荷守恒(2)再将B接地，电荷的分布。内表面电荷为-qA接地时，外表面电荷设为Q设B的电量为根据孤立导体电荷守恒例3求(1)(2)B球圆心处的电势总结(有导体存在时静电场的计算方法)1.静电平衡的条件和性质:

2.电荷守恒定律3.确定电荷分布,然后求解静电感应电晕放电可靠接地带电云避雷针的工作原理++++－－－－－++－+5ElectrostaticScreening静电屏蔽ElectrostaticScreening:InsulatingtheinfluenceofelectricfieldusingconductorshellNomatterthechangeofchargeAtheforceonBchargealwaysiszero.A电荷变化,B电荷受力总是为零。Thechargeinsideshellcanbeshielded壳可以屏蔽内部IfthechargeBischanged,theforceonthechargeAischangedtoo.B电荷变化，A电荷受力会变化。ThechargeAoutsideshellcannotbeshielded壳不能屏蔽外边电荷A。A。BIftheshellistheground,theinfluencebetweenAandBisnotexist.接地导体壳，可以使壳内外的电荷彼此不影响。用空腔导体屏蔽外电场++++++++接地空腔导体屏蔽内电场腔外电场不影响腔内腔内电场不影响腔外电介质中不存在自由电荷，在电场中会发生极化现象。极性介质：HCl、SO2、H2O等，非极性介质：O2H2CO2§2DielectricsandDielectricPolarization无极分子：（氢、甲烷、石蜡等）有极分子：（水、有机玻璃等）电介质1Dielectricpolarization无外电场时，电偶极矩取向杂乱或为零，整个介质呈电中性。当有外电场时，非极性分子产生极化，极性分子趋向外场排列，介质表面产生束缚电荷。E----+-+-+-+-+-+-+-+-+-+-+-+束缚电荷´E0E-+-+-+-+-+-+-+-+-+-+-+-+束缚电荷´E0E位移极化取向极化无极分子电介质有极分子电介质2Polarization极化的强弱程度用电极化强度矢量描述。由于每个分子为偶极子，偶极矩P越大，单位体积内偶极子越多，极化越强。3极化电荷与自由电荷的关系对无限大均匀带电平板：线性各向同性介质+++++++++++----------------+++++解：QR例1一点电荷Q被半径为R的介质1包围，球外是2的介质，求空间电场强度。例2平行极板间极化强度矢量，求介质表面束缚电荷密度解：选取圆柱形高斯面return110-310-610-910-12FmFF微nF纳pF皮1ThecapacitanceofanIsolatedConductorUnit：Farads法拉TheradiusoftheearthR＝6370kmC=7.08×10-4F§3CapacitanceCapacitorCapacitanceisameasureofamountofchargeaconductorholdsatagivenpotentialdifference电容是一个导体被给定电势差时所能容纳的电荷量的测量2CapacitanceofaCapacitorCapacitor：Itisconsistsoftwoconductorplatesbeingveryclosed（1）电容器分类按形状：柱型、球型、平行板电容器按型式：固定、可变、半可变电容器按介质：空气、塑料、云母、陶瓷等（2）电容器电容特点：非孤立导体，由两极板组成4CalculatingtheCapacitanceofaCapacitor(1)AParallel-plateCapacitorThecapacitanceofacapacitordependsontheseparationdistanced,theareaSandthepermittivityεRARBq-qSD=0-QdABQ(2)ASphericalCapacitor(3)ACylindricalCapacitor-取高为h圆柱形高斯面RARBr

hNote：1Thecapacitanceofacapacitordependsonthegeometryofthecapacitorandthepermittivityε,independentof

thepotentialdifferenceandthecharge2ThesphericalcapacitorisastandardcapacitorEx1Aparallel-platecapacitorconsistsoftwosquareplates,eachofsides4.0cmseparatedby2.0mm.(a)Calculatethecapacitance.(b)Howmanyelectronscanbestoredonaplateifthecapacitorischargedto50V?Solution(a)(b)Q=CU=7.1×10-12×50=3.5×10-10CThemagnitudeofthechargeofoneelectronis1.6×10-19C,sothenumberNofelectronsthatcanbestoredis=7.1×10-12F=7.1pF.1EnergystorageinacapacitorElectricpotentialenergyisrelatedtotheworkdowninmovingachargeinanelectricfield.Theamountofworkdonetoassemblethechargeisequaltothepotentialenergystoredinthesystem.Foraparallel-platecapacitor:CStart:Nocharge;End:-Q,+Q.Atamoment:-q,qTheworkisequaltothetotalenergystoredinthecapacitor§4TheEnergyofElectricfieldTheworkdonetomovethechargedqfromAtoBAB2ThedensityofelectricfieldenergyTheenergystoredinacapacitorisintheformofelectricpotentialenergy.Whereistheenergy?Considerthespecificexampleofaparallel-platecapacitorItmeansthattheenergyisstoredintheelectricfield.Althoughthisdiscussionreferstoaparallel-platecapacitor,theconceptofenergydensityisdefinedbythesameequationforcapacitorsofanyshapeEnergydensity:theenergyperunitvolumeForacapacitorofanyshape,theenergystored解1用电场能量公式:在r处取半径为r,r+dr的球壳,在球壳内电场能量:解2导体球电容公式:例求半径为R,带电为+Q的导体球所具有的静电能..B.A问题带电平行板电容器充满均匀介质,中间挖去一扁平的圆柱,A点和B点的D和E谁大?答案:EA>EBDA=DBreturn§5Application例1无限长均匀带电圆柱面内外的场强分布：>0，R面内面外方向垂直柱面向外解：电荷分布具有柱对称性，电场分布具有柱对称性；利用高斯定理求场强分布，选取柱形高斯面rR

例2无限长均匀带电圆柱体内外的场强分布：>0，R柱体内柱体外方向垂直圆柱体轴线向外方向垂直圆柱体轴线向外rR

例3无限长均匀带电圆柱面，半径为R，单位长带电量为+，试求其电势分布。解：电场强度分布：r>R：r<R：

P1P2••电场强度方向垂直于带电圆柱面沿径向。若仍选取无穷远处为电势零点，则导致电势为无穷大选取距轴线nR处为零电势点：

例4如图，在一电荷体密度为的均匀带电介质球体中，挖出一个以O’为球心的球状小空腔。试证：球形空腔内的电场是均匀电场，其表达式为：证明：用填补法证明。介质球在空腔内任一点的场为：P点的合场强：••OO’空间任意一点