《E6导体与电介质》PPT课件.ppt

1ConductorsintheElectrostaticField,2DielectricsandPolarizationintheElectricField,3CapacitanceandCapacitor,4TheEnergyofElectricfield,Chapter6ConductorsandDielectricsintheElectrostaticField,5Application,1Electrostaticinduction,1ConductorsintheElectrostaticField,+,2ElectrostaticEquilibrium,Inelectrostaticequilibrium,allthefreeelectronareatrest.达到静电平衡时，所有自由电子都处于静止状态。,3ConditionsofElectrostaticEquilibriumTheelectricfieldiszeroinsideaconductor导体内部任何一点处的电场强度为零,Corollary1Theconducingsurfaceisanequipotentialsurface,andallpointsintheinteriorareatthesamepotentialasthesurface,导体表面是等势面，导体是等势体Corollary2Thefieldatthesurfaceoftheconductor(andjustoutside)isperpendiculartothesurface,Proving1,Notangentialcomponentcanexist。导体表面附近电场强度垂直于等势面。,Proving2,3DistributionofChargea)Allofthechargesisonthesurfaceoftheconductor,Prove：,b)Theelectricfieldonthesurfaceofaconductor,Note:,Thefieldatthesurfaceoftheconductor(andjustoutside),c)DistributionofChargeofSphericalConductor,Restrictingfactors：theelectricfieldiszeroinsideaconductor.,Conductorshell（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.,ItisdeterminedbyGaussslaw.,如图所示,导体球附近有一点电荷q。,解,O点的电势为0，等于Q和q在该点的电势之和。,接地后导体上感应电荷的电量。,设感应电量为Q,例1,求,-,-,-,q在O点的电势,Q在O点的电势,O点的电势为0,两球半径分别为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,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,-q,电荷守恒,(2)再将B接地，电荷的分布。,内表面电荷为-q,A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,带电导体尖端附近的电场特别大，可使尖端附近的空气发生电离而成为导体产生放电现象,尖端放电现象,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:Insulatingtheinfluenceofelectricfieldusingconductorshell,NomatterthechangeofchargeAtheforceonBchargealwaysiszero.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,Iftheshellistheground,theinfluencebetweenAandBisnotexist.,接地导体壳，可以使壳内外的电荷彼此不影响。,腔外电场不影响腔内,腔内电场不影响腔外,例：球形壳C，电荷A带q,B带Q，r远大于R。求:A，B，C彼此之作用力。,解：(1)A、B之间作用力：,(2)A、C对B来说是带电量q的点电荷，B受力：,(3)静电屏蔽，A受力F=0,(4)A、C之间作用力：,(5)B、C之间作用力F0,(6)C接地，A、B受力为零,问题：导体壳是否真的能够屏蔽掉外电场使其不能进入腔内？,答：接地导体壳,return,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。,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,束缚电荷,E0,E,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,-+,束缚电荷,E0,E,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,+,-,3Therelationshipbetweenelectricpolarizationandboundcharge,4ElectricdisplacementGaussslawinmedium,Electricdisplacement电位移矢量,Relativepermittivity相对电容率,Thefieldinmedium介质中的场：,(Absolute)permittivity电容率,解：,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,return,110-310-610-910-12FmFF微nF纳pF皮,1ThecapacitanceofanIsolatedConductor,Unit：Farads法拉,TheradiusoftheearthR6370km,C=7.0810-4F,3CapacitanceCapacitor,Capacitanceisameasureofamountofchargeaconductorholdsatagivenpotentialdifference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,2CapacitanceofaCapacitor,Capacitor：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,3CombinationsofCapacitors电容器的联接,(1)ConnectedinSeries串联,(2)ConnectedinParallel并联,Forcapacitorsconnectedinseriesthechargeoneachcapacitoristhesame.,CapacitorsconnectedinParallelhavethesamepotentialdifferenceacrosstheirplate,Comparing弹簧的串并联，电阻的串并联，物理中由几个相同量纲量组成另一个同量纲量时，只有上面的组合。,4CalculatingtheCapacitanceofaCapacitor,(1)AParallel-plateCapacitor,Thecapacitanceofacapacitordependsontheseparationdistanced,theareaSandthepermittivity,(2)ASphericalCapacitor,(3)ACylindricalCapacitor,-,取高为h圆柱形高斯面,Note：1Thecapacitanceofacapacitordependsonthegeometryofthecapacitorandthepermittivity,independentofthepotentialdifferenceandthecharge2Thesphericalcapacitorisastandardcapacitor,Ex1Aparallel-platecapacitorconsistsoftwosquareplates,eachofsides4.0cmseparatedby2.0mm.,(a)Calculatethecapacitance.,(b)Howmanyelectronscanbestoredonaplateifthecapacitorischargedto50V?,Solution(a),(b)Q=CU=7.110-1250=3.510-10C,Themagnitudeofthechargeofoneelectronis1.610-19C,sothenumberNofelectronsthatcanbestoredis,=7.110-12F=7.1pF.,Ex2Asphericalcapacitorconsistsoftwothinconcentricsphericalshellsofradiiaandb,withab.AchargeQisplacedontheinnershell,andQontheoutershell,whichisgrounded.Calculatethecapacitance.,InordertouseC=,weneedfirsttocalculatethepotentialdifferencebetweentheshells,whichinturndependsonthefield.Aconcentricsphereofradiusr,wherea0，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,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,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：,rR：,rQB：（1）证明两板内侧电荷密度符号相反，数值相等；外侧的电荷密度符号相同，数值相等。（2）计算板上的电荷面密度和两板间的电势差。,解：(1)证明,（2）电荷守恒定律：,AB,QAQB,d,P1,P2,P1：,静电平衡导体内部场强为零,A、B间总场：,例6把一块原来不带电的大金属板B移近一块带电Q的A板，B接地和不接地，两极板