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1、Chapter 3,Conductors in electrostatic field & capacitors,物理学中册，马文蔚改编,P56-99,Contents in this chapter:,* 1)Conductors in electrostatic equilibrium 导体静电平衡,2) Electric properties of conductors and dielectrics in E filed. 电场中导体和电介质的电学性质,* 3) Gausss law with dielectrics 有介质时的高斯定理,* 4) Properties and calc
2、ulation of capacitors. 电容器的性质和计算,5) Energy of electrostatic field 静电场的能量,3.1 conductors in electrostatic field,recall,Induction 感应,Induction process of a conductor in E field 导体在静电场中的感应过程,(a) Conductor without external E field,(b) Conductor in an external E field (at the beginning),Induced charge,In
3、duced charge,(c) Conductor in an external E field (at equilibrium),Properties of an isolated conductor in electrostatic equilibrium 孤立导体静电平衡时的性质,The E field is zero everywhere inside the conductor. 导体内部电场处处为零。,Reasoning:,The conductor is in electrostatic equilibrium.,2) If the isolated conductor car
4、ries a net charge, the net charge resides entirely on its surface. 如果导体本身带有净电荷，那么这些净电荷将全部分布在 导体表面。,Reasoning:,Gausss law,Both the net charge and the induced charge reside on the Surface.净电荷和感应电荷都分布在表面上。,S is an arbitrary Gaussian surface inside the conductor.,3) The E field on the surface of the cha
5、rged conductoris perpendicular to the conductor surface and has a magnitude , where is the surface charge density at that point. 导体表面的电场与表面垂直，大小为 。,Reasoning:,Gausss law,S is a small Gaussian surface, whose end faces parallel to the surface of the conductor.,The E field is perpendicular to the surfa
6、ce because the conductor is in electrostatic equilibrium.,The magnitude of the E field on the conductor surface is:,Reasoning:,Gausss law,Example,one uniform E field,the E field after a metal ball was put into the field (in equilibrium),4) On an irregularly shaped conductor, the surface charge densi
7、ty is highest at locations where the radius of curvature of the surface is smallest. 不规则形状导体曲率半径最小的地方表面电荷密度最大。,越尖的地方感应电场越强。,尖端放电,5) The surface of the conductor in electrostatic equilibriumis an equi-potential surface and the conductor is an equi-potential body. 处于静电平衡的导体的表面是一等势面，导体是一等势体。,Reasoning:
8、,Take one arbitrary path from point A to point B inside the conductor, the E potential difference between the two points is:,Applications of properties of conductors in electrostatic Equilibrium导体静电平衡性质的应用,1) Discharge 放电,Losing charges of charged particle/object. 带电物体失去电荷。,Link: the atmospheric E f
9、ield & lightening,了解：大气电场和闪电,There is a huge E field in the atmosphere of the Earth.,The Earth is a good conductor.,The average magnitude of the E field at the surface of the Earth is:,Very strong E fields in the thundercloud cause lightening discharge between the cloud and the ground.,Typical E fie
10、lds during a thunderstorm are as high as 25000N/C.,2) Electrostatic shielding 静电屏蔽,Cavity conductor空腔导体,No net charges inside the cavity conductor空腔导体无净电荷,The external E field has no effect on the space inside the cavity. 外电场对空腔内部无影响。可将仪器等放入空腔内部起到屏蔽作用。,b) There is net charges inside the cavity condu
11、ctor空腔内有净电荷,* The external E field has no effect on E field inside the cavity. 腔内电场不受外电场影响。,Gausss law,由于导体内表面上电量与腔内电荷等量异号，在发出的电场线全部终止在内表面上，则及在腔外产生的合场强为。,* The external E field does not depend on the E field inside the cavity. 腔外电场也不受腔内电场的影响。It does not relate to the charge distribution inside the c
12、avity, but the charge quantity. 外电场与腔内电荷分布无关，但与腔内带电体电量有关。,The external E field is the superposition of the E fields due to Q+q.导体外的电场是产生的电场的叠加。,外表面电荷全部流入地下，导体外部由产生的电场随之消失。,* If connect the external surface of the cavity to the ground, the external E field does not relate to E field inside the cavity
13、. 如果腔外表面接地，则外场不受腔内电场影响。,Summary: the charge distribution of a conductor in electrostatic equilibrium,小结： 静电平衡导体的电荷分布,1) No charges inside the conductor 导体内部无电荷,Net charges entirely on the external surface.静电荷全部位于外表面,2) cavity conductors with charges空腔导体带电荷Q,a) There is no charges inside the cavity c
14、onductor空腔导体内部无电荷,b) There is charges inside the cavity conductor空腔导体内部有电荷,Example 3-1,As shown in the figure, there are one ball A and its coaxial spherical shell B. The radius of the ball is R1. The inner and outer radii of the spherical shell are R2 and R3 respectively. The charge on the ball is
15、q and Q on external surface of the shell.,Find: 1) the charge in the space. 2) the E field in the space. 3) the potential in the space. 4)if connect A and B with a wire, calculate 1), 2) and 3).,Solution:,1) since the ball and the shell will arrive electrostatic equilibrium, we can get the charge di
16、stribution in the space as following:,q: on the surface of the core,-q: on the inner surface of the shell,Q+q: on the outer surface of the shell,2) according to Gausss law, the E field in the space is:,0,3) the potential of the core:,3) the potential of the shell:,4) if connect A and B with a wire,the charge on the surface of the core and the charge on the inner surface of the shell are neutralized. There is no charge inside the shell.,
