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习题3第6题：求上半平面内静电场的点位，即解下列定界问题。 0lim),()0 ,(, 0, 0222uxxfxuxyuyx0),(dd),(222yUyyUyyBeAeyU),(yCe)()0 ,(FUyeFyU)(),(ex221yexyy221ttxytfyyxud1)(),(22第1页/共16页0,20, 0),(20 ,),()0 ,(0,20 ,1122222222ttRuRutRuuuauatu1,1)0 ,(0, 0), 1 (0, 1,12222uttutuuatuTu TTaT12 12TaT02TaT022 0) 1 ()0(), 0(tu自然边界条件 第2页/共16页1,1)0 ,(0, 0), 1 (0, 1,12222uttutuuatu022 0) 1 ()0(002 lnBA002)()(00BYAJ)(0AJ0)() 1 (0AJ)0(n, 3 , 2 , 1,2)0(nnn)()0(0nnnJA0222 02)j ()j (00BYAJ0j222 02TaT022)0(nnnTaTtannneBT22)0(1)0(022)0()(ntannneJCu1)0(02)()0 ,(1nnnJCu)(21d)(1)0(2110)0(02nnnJJC1)0(13)0()0(0)()(822)0(nnntanJeJun)(8)0(13)0(nnJmnmmnxmnmxJ202) 1(!) 1()(022 yxyxyx)()(00 xBYxAJyyx第3页/共16页RRtuuttRutRuuatu,1)0 ,(, 0)0 ,(0, 0),(0,12222222Tu TTaT12 12TaT02 TaT0222 )0(, 0)(R002 lnBA00A02)()(00BYAJ)(0AJ)()(0RJARRn)1(, 3 , 2 , 1,2)1(nRnn)()1(0RJAnnn022 0)(1RJA), 0(tu02)j ()j (00BYAJ0j222 第4页/共16页RRtuuttRutRuuatu,1)0 ,(, 0)0 ,(0, 0),(0,1222222202 TaT0000A, 3 , 2 , 1,2)1(nRnn)()1(0RJAnnn000 T000DtCT0D0)0(0T00T0022)1( nnnTaRTatRDatRCTnnnnn)1()1(sincos1)1(0)1()1()(sincosnnnnnnRJatRFatREu)(sincos)1(0)1()1(RJAatRDatRCTunnnnnnnnn)(sincos)1(0)1()1(RJatRFatREnnnnn第5页/共16页RRtuuttRutRuuatu,1) 0 ,(, 0) 0 ,(0, 0),(0,122222221)1(0)1()1()(sincosnnnnnnRJatRFatREu0)0 ,(u0nE1)1(0)1()(sinnnnnRJRatFu221)1(0)1(1)()0 ,(RRJRaFtunnnn)(2d)(1)1(202)1(0)1(022nnRnnJRRaRJRFrrRJrRrJRkmd0)1(0)1(0rRrJRrRJRmmRkm)1(1)1(0)1(02)1(drRJrRrJRrRrJRrRJRkRmmmmkm)1(00)1(1)1()1(1)1()1(02)1(drrRJrRrJkRmmkd)1(10)1(1)1()1(kmJRkmm),(2, 0)1(202rRrRJrRrJRRmRkmmm)1(0)1(0)1(0)1(2)1(d第6页/共16页RRtuuttRutRuuatu,1) 0 ,(, 0) 0 ,(0, 0),(0,122222221)1(0)1()(sinnnnnRJRatFu)(2d)(1)1(202)1(0)1(022nnRnnJRRaRJRF)1(002)1(22)1(2)1(20)1(d)(1)(2ntttJtRRJannnn)1(022)1(205)1()(d)(4ntJtJaRnn)1(012)1(2)1(203)1()(d1)(2nttJtJaRnnn)1(02)1(1)1(203)1(d2)()(2nttttJJaRnnn)(4)1(03)1(nnJaR)()(4)1(22)1()1(205)1(nnnnJJaR0)(2)()()1(1)1()1(2)1(0nnnnJJJ1)1(0)1()1(03)1()(sin)(14nnnnnRJRatJaR第7页/共16页aAhuuhzzauhzazuuu0,),(, 0)0 ,(0, 0),(0 ,0, 012222Zu01 ZZZ ZZ1022 0 ZZ002 lnBA0020222 )()(00BYAJ)(0AJ0)(0aAJ)0(1nna2)0(21nna)()0(0aJAnnn0j220j222 )j ()j (00BYAJ第8页/共16页2)0(21nna)()0(0aJAnnn012)0(2 nnnZaZzanzannnneDeCZ)0()0(1)0(0)()0()0(nnzanzanaJeFeEunn0)()0 ,(1)0(0nnnnaJFEu0nnFE1)0(0)()0()0(nnzazanaJeeEunn1)0(0)0()(sh2nnnnaJzaEaAhuuhzzauhzazuuu0,),(, 0)0 ,(0, 0),(0 ,0, 012222第9页/共16页AaJhaEhunnnn1)0(0)0()(sh2),()0(2120)0(0)0(2d)(sh2nannnJaaJAhaE1)0(0)0()(sh2nnnnaJzaEu)0(002)0()0(212d)(2ntttJaJaAnn)0(012)0()0(21)(d2nttJJAnn)(2)0(1)0(2)0()0(21nnnnJJA)0()0(12nnJA1)0(0)0()0()0()0(1)(shsh2nnnnnnaJzahaJAuaAhuuhzzauhzazuuu0,),(, 0)0 ,(0, 0),(0 ,0, 012222第10页/共16页0,20, 0),(20 ,),()0 ,(0,20 ,11222222ttRuRutRuuuatuTu TTTaT2211 2211TaT02TaT022 22022 0 )2()0(2n, 3 , 2 , 1 , 0nnBnAnnnsincos0222 n0)(R)0()(nnJC)(nmR2)(Rnmmn)()(RJCnmnmnmn, 3 , 2 , 1m)()(nnnnYDJC第11页/共16页0,20, 0),(20 ,),()0 ,(0,20 ,11222222ttRuRutRuuuatunBnAnnnsincos, 3 , 2 , 1 , 0n)()(RJCnmnmnmn, 3 , 2 , 1mtaRmnmnnmeET22)(022)(mnnmmnTaRTtaRnmnmnmnmnnmnmnnmeRJnGnFTu22)()(sincos)(01)(0122)()(sincosnmtaRnmnmnmnnmmnnmeRJnGnFuu),(nmfdcos),(120nnmfFmn0nd ),(21200nmfFmdsin),(120nnmfGmn)(2d)(),(sincos)(2120)(0nmnRnmnnmnmnJRRJnGnF第12页/共16页1, 0)0 ,(,1)0 ,(0, 0),(0,1222222tuRuttRutRBuutu)(),(WtVuBWW 1BEE 222*EW 2*4BWlnDCW24lnBDCW24BC 04)(2RBCRW24RBC 2244BRBW0, 0),(0, 0)0 ,(,441)0 ,(0,0,122222222ttRVRtBRBRVtRVVtV第13页/共16页1, 0)0 ,(,1)0 ,(0, 0),(0,1222222tuRuttRutRBuutu1)0(0)()(nnnRJtvuBRJRtvRJRtvRJtvnnnnnnnnnnn 1)0(0)0(1)0(02)0(1)0(0)()(1)()()()(1)0(0)(nnnRJB0)()()(2)()(1)()()0(0)0()0(1)0(0)0()0(02)0( RJtvJBRJRtvRJRtvnnnnnnnnnn0)()()()(2)()()0(02)0()0(1)0(0)0()0(022)0( RJtvtvJBRJRRJRnnnnnnnnn0222 ynxyxyxRnnnRJJRBB0)0(0)0(212d)()(2)0()0(1)(2nnJB2)0()0()0(1)()()(2 RtvtvJBnnnnn0)(2)()()0()0(12)0( nnnnnJBtvRtv第14页/共16页1, 0)0 ,(,1)0 ,(0, 0),(0,1222222tuRuttRutRBuutu1)0(0)()(nnnRJtvu0)0(nvRnnnRJRJRv0)0(022)0(212d)(1)(21)0(3)0()0(1)(8nnJ0)(2)()()0()0(12)0( nnnnnJBtvRtvtRJBRtRJtvnnnnnnn)0(2)0()0(1)0(3)0()0(1sin)(2cos)(8)(第15页/共16页感谢您的观看！第16页/共16页
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