E导体与电介质PPT学习教案

1、会计学1E导体与电介质导体与电介质3 Distribution of Chargea) All of the charges is on the surface of the conductor Prove：0E)(0dSSE0iiqb) The electric field on the surface of a conductor s0E0ESE0dqSE 侧侧上上下下SEd0/ssENote:0EThe field at the surface of the conductor (and just outside)c) Distribution of Charge of Spherica

2、l ConductorRestricting factors：the electric field is zero inside a conductor.0E第1页/共23页E=0q4Conductor shell（腔）（腔）(1) No charge in a conductor shell a The electric field is zero inside inside conductor and shell 导体内、空腔内场强皆为导体内、空腔内场强皆为零；零；b The conductor and shell are equipotential 导体、空腔为等势体；导体、空腔为等势体

3、；c The charge must lie on the surface 内表面处处没有电荷，电荷只分布在外表面内表面处处没有电荷，电荷只分布在外表面.(2) A charge q in a conductor shell On the inner surface of the shell the charge is - q.On the outer surface of the shell the charge is q. It is determined by Gausss law.第2页/共23页5 Electrostatic Screening 静电屏蔽静电屏蔽Electrostat

4、ic Screening: Insulating the influence of electric field using conductor shell No matter the change of charge A the force on B charge always is zero. A电荷变化电荷变化,B电荷受力总是为电荷受力总是为零。零。The charge inside shell can be shielded 壳可以屏壳可以屏蔽内部蔽内部If the charge B is changed, the force on the charge A is changed to

5、o.B电荷变化，电荷变化，A电荷受力会变化。电荷受力会变化。The charge A outside shell can not be shielded 壳不能屏蔽外边电壳不能屏蔽外边电荷荷A 。A。BIf the shell is the ground, the influence between A and B is not exist.接地导体壳，可以使壳内外的电荷彼此不影响。接地导体壳，可以使壳内外的电荷彼此不影响。第3页/共23页例：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：解：(1) A、B之间作用力：之间作用力：204rQqF(2) A、C

6、对对B来说是带电量来说是带电量q的点电荷，的点电荷，B受力：受力：204rQqF(3) 静电屏蔽，静电屏蔽，A受力受力 F=0+QBA +q CrR(4) A、C之间作用力：之间作用力：2024RqF(5) B、C之间作用力之间作用力F0(6) C接地，接地，A、B受力为零受力为零问题：导体壳是否真的能够屏蔽掉外电场使其不能进入腔内？答：接地导体壳答：接地导体壳return第4页/共23页电介质中不存在自由电荷，在电场中会发生极化现象。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：极性介质：HCl、SO2、H2O 非极性介质：非极性介质：O O2 2 H H2 2 CO CO2 2

7、1 Dielectric polarization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- - - 2 Polarization 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。PEP0线性各向同性介质线性各向同性介质2 Dielectrics and Dielectric Polarization VpP第5页/共23页3 The relationship between electric polarization and bound cha

8、rge)()(dinSboundSqSP4 Electric displacement Gausss law in medium 00/ )(/dfreeboundSqqqSE freeSqSPEd)(0PED0freeSqSD)(dElectric displacement 电位移矢量电位移矢量EP0ED0)1 (EEDr0:rRelative permittivity 相对电容率相对电容率EDqfreeThe field in medium 介质中的场：介质中的场：:(Absolute) permittivity 电容率电容率第6页/共23页解：解：QR12QrDsdDs2)(424 rQ

9、D)(421RrnrQEED/DE)(422RrnrQE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。束缚例2 平行极板间极化强度矢量 ，求介质表面束缚电荷密度P解：解：束缚iboundqSPdPbound选取圆柱形高斯面选取圆柱形高斯面PSSPboundreturn第7页/共23页1 10-3 10-6 10-9 10-12F mF F微 nF纳 pF皮RQU041 The capacitance of an Isolated ConductorUQCRQCRQ0440Unit： Farads 法拉The radius of the earth R6370kmC

10、=7.0810-4F3 Capacitance Capacitor Capacitance is a measure of amount of charge a conductor holds at a given potential difference 2 Capacitance of a CapacitorCapacitor：It is consists of two conductor plates being very closed BAUUQC第8页/共23页3 Combinations of Capacitors 电容器的联接电容器的联接CQCCQCQCQUUU21212111(

11、1) Connected in Series 串联(2) Connected in Parallel 并联并联CUUCCUCUCQQQ)(212121For capacitors connected in series the charge on each capacitor is the same.C1 C2 21111CCCC1 C2Capacitors connected in Parallel have the same potential difference across their plate21CCCComparing 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

12、个同量纲量时，只有上面的组合。第9页/共23页4 Calculating the Capacitance of a Capacitor(1) A Parallel-plate CapacitorSSDfreeSQD/SQDESQdEdUUBAdSUUQCBAThe capacitance of a capacitor depends on the separation distance d, the area S and the permittivity24 rqDBARRq114RARBq-qSD=0-QdABQ)(4ABBAbaRRRRUUqCBARRBAlEUUd24rqDE(2) A

13、Spherical Capacitor第10页/共23页(3) A Cylindrical Capacitor - QhrDSDS2drDE2rD2ABBABARRlEUUln2d取高为取高为h 圆柱形高斯圆柱形高斯面面hQRARBr hABbaRRhUUqCln2Note：1 The capacitance of a capacitor depends on the geometry of the capacitor and the permittivity, independent of the potential difference and the charge 2 The spher

14、ical capacitor is a standard capacitor第11页/共23页Ex1 A parallel-plate capacitor consists of two square plates, each of sides 4.0 cm separated by 2.0 mm.(a) Calculate the capacitance.(b) How many electrons can be stored on a plate if the capacitor is charged to 50 V?Solution (a)43120100 . 40 . 4100 . 2

15、1085. 8SdC (b) Q=CU = 7.110-1250=3.510-10 CThe magnitude of the charge of one electron is 1.610-19 C, so the number N of electrons that can be stored is91912102 . 2)106 . 1 ()105 . 3(eQN=7.1 10-12 F=7.1pF.第12页/共23页 Ex2 A spherical capacitor consists of two thin concentric spherical shells of radii a

16、 and b, with ab.A charge Q is placed on the inner shell, and Q on the outer shell, which is grounded. Calculate the capacitance.abQQ In order to use C= , we need first to calculate the potential difference between the shells, which in turn depends on the field.A concentric sphere of radius r,where a

17、rEB DA=DBreturn第16页/共23页5 Application例例1 无限长均匀带电圆柱面内外的场强分布： 0 ，R L)2()1()()(底底侧SdESdESdESdES00SErLS2面内面内0q0E面外面外LqrE02方向垂直柱面向外解：电荷分布具有柱对称性，解：电荷分布具有柱对称性， 电场分布具有柱对称性；电场分布具有柱对称性；利用高斯定理求场强分布，利用高斯定理求场强分布，选取柱形高斯面选取柱形高斯面ErR第17页/共23页 例例2 无限长均匀带电圆柱体内外的场强分布： 0 ，R L00SELrS)2(12柱体内柱体内Lrq21012rE 柱体外柱体外LRq220222rRE方向垂直圆柱体轴线向外方向垂直圆柱体轴线向外ErR)2()1()()(底底侧SdESdESdESdES第18页/共23页 例例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：解：电场强度分布：rE02rR：0ErQB：（1） 证明两板内侧电荷密度符号相反，数值相等