大学物理：06静电场-2导体和介质

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1、AB无外电场无外电场加外电场：电子在电场力作用下运动加外电场：电子在电场力作用下运动导体的静电感应过程导体的静电感应过程0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应 E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应 E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应 E0E导体的静电感应过程导体的静电感应过程

2、0E外场外场感应感应E0E导体的静电感应过程导体的静电感应过程0E外场外场感应感应 E0E导体的静电感应过程导体的静电感应过程E静电平衡状态静电平衡状态0E E00EEEl静电平衡条件：静电平衡条件：0内E表面表E0E E00EEEbabaUUlEdabU0E0 UlEd0d lE0U静电平衡的导体是等势体静电平衡的导体是等势体PSSSE0d0内Siq 0EQSSSE0d0E0内SiqS内无净电荷存在内无净电荷存在QbabaUUlEd0baUU abqQqqPSSSESSEdSSEdSE0S0ERrQqRrRQUR041RRR02440RRrqUr0410rrrRRr0RRRU0rrrU 0E

3、AARO q qqdxEEE0EE 0)(420idqidq20404dqRqU0RO q qqd0UUUdq04RqdqU0100440qdRq1ROqd1qURO q qqd12341P2PiEp)2222(0403020110iEp)2222(040302012413204132x1234qS)(21qS)(43SqSq43210 x04321041电荷分布在极板内侧面电荷分布在极板内侧面Sq2Sq33241iE)22(03021iE)22(03022iSq023123x14003EqS)(210)()(4321032qS)(43Sq41413223123x14iE)22(04011iS

4、q0iE)22(040120iE)22(04013iSq014123xSq41 Sqq2141Sqq22141112SqSqq21223Sq121Sq24312Sqq22114123234132xiE)2222(040302011iE)2222(040302012iE)2222(040302013i01iSqq0212i02iSqq0212i01iSqq0212Sqq2)(211Sqq22121412323x1r2r3r1rr 21rrr32rrr3rr 1r2r3rqqqQ01E02024rrqE03E02044rrQqE1d1rrEU321d4d42020rrrrrQqrrq321041r

5、Qqrqrq321dd42rrrrErE02024rrqE02044rrQqE1r2r3rqqqQ3d2rrEU3d4rrE3d420rrrQq304rQq21UUU210114rrq1r2r3rqqqQ3210141rQqrqrqU02044rrQqE0321EEE02044rrQqE3d421rrEUUrrQqrd4320304rQq02024rrqE0431EEEqq21d21rrrEU)11(4210rrq21UUU1U3020101444rQqrqrqU0Qrrrrrrrrq12231312 q q qQ3024rQqU q q qQ1323210124rrrrrrrrQQrrrrr

6、rrrq122313120ep甲烷甲烷 CH4HHHHC水水 H2OHHOep0ep0E0Eep转向极化转向极化1f2f0E0Eep0ip0ipipVpPiPlnnPlSdPlqpidlSdVipPdcoslSVcosddcosPnPnP000lSPidPnnPlSdSSqddSPdcosSPdsqqd外sSPdPSdn内外SqqSSPdPEPe0PE PEEEE00EEEEEE EEE0000E EPPn EPe0eEE10er1相对介电系数相对介电系数rEE00E 部分抵消部分抵消 的缘故的缘故E0E SSqSE内01d内内SSqq)(100内SSqSPE00dSSSPqd内PED0SSq

7、SD内0d电位移矢量电位移矢量有介质时有介质时(或或 )的高斯定理的高斯定理D内SSqSD0dSSDdDEDF ED E DPED，EPe0PED0EEDe00Ee)1(0Er0r0ED介质的介电常数介质的介电常数er1(1)DEDPED，R0qrSrDSD24d0q204 rqD0204rrqDDErD002004rrqrR0qrEPe0020004)1(rrqrr02041rrqrrnPP2041RqrrR0qrnP02004rrqErer1nP24 Rq 011qrq与与q0反号，且数值反号，且数值小于小于q02041RqrrR0qr221111r0V0E1D1E2D2E221111r1

8、D1E2D2E 00ESSSDd1SDd1下底SDSd1SD1dEV00S10V0E11DrDE01122DdEdE2121EE r12r01022DE 221111r1D1E2D2ES02SD 1S1SSS2221221rr121r1225852221111r1D1E2D2ESr120221EE052052EdEV1dE05230052V1201011EPrnp110056E56561 P561P522581221111r1D1E2D2ES00EUqC 孤立导体的电容孤立导体的电容ABqqAUBUl定义定义:BAUUqC电容器的电容电容器的电容qABrSdqEBABAlEUUdEdSqdr0

9、Sqr0BAUUqCdSr0ABARBRlrrEr02BABAlEUUdBARRrEdBARRrrrd20ABrRRln20ABrBARRUUln20BAUUqCABrRRlln20ABrRRlln20ABARBRlr204rqErBRARABrBABAlEUUd)11(40BArRRqBARRrEdBAUUqCABBArRRRR04dSCr0平板ABrRRlCln20圆柱ABBArRRRRC04球1.并联并联:1C2C3CnCUUqC Uqqqn21nCCC21niiC12.串联串联:UUqCnUUUq21nCqCqCqq/21nCCCC111121niiC11niiCC1并niiCC111

10、串R3R2R1r1r2021014rrQEr022024rrQEr(R2 r R3)(R1 r R2)31dRRlEU3221dd21RRRRlElER3R2R1r1r2021014rrQEr022024rrQEr)11(1)11(143222110RRRRQrrUQC)11(1)11(143222110RRRRrrR3R2R1r1r221111CCCABBArRRRRC04球2121CCCCC12211014RRRRCr23322024RRRRCrdCCCdrr111d2d3dd1C2C3CC201dSC102dSCr303dSC133221321CCCCCCCCCC3211111CCCC3

11、210dddSrr1d2d3dd132ddddddCSdrr)1(101dCCrr11dCCCrr11d2d3dd3210dddSCrr331221dEdEdEU301020dddrUqC US3210dddSrr同样可证同样可证1d2d3ddabqdqqE)(ddbaUUqAqCqdQqCqW0dCQ2212)(21baUUC)(21baUUQUQC2)(21baUUCW2)(21EddSVE 221VWwe221EDE21EDVwWeVdVDEVd212)(21baUUCWrSdVDEWVd210内E02041rrQE外Rr Rr QRVeVwWdVVE d2120RrrrQd4)4(2122200RQ2081d dddSC0UCQddSU0221UCW 2021UddSd d2)(21baUUCWdSC0 d 21 2CQW 220)(21UddSd WWA220)(21UdddS2021UddSW220)(21UddSdWd dd电场是能量携带者的观点电场是能量携带者的观点EewVW)(VVwe)(2120ddSSdEdSE2021220)(21UdddS WWAddUE