《E6导体与电介质》PPT课件.ppt

1 Conductors in the Electrostatic Field,2 Dielectrics and Polarization in the Electric Field,3 Capacitance and Capacitor,4 The Energy of Electric field,Chapter 6 Conductors and Dielectrics in the Electrostatic Field,5 Application,1 Electrostatic induction,1 Conductors in the Electrostatic Field,+,2 Electrostatic Equilibrium,In electrostatic equilibrium, all the free electron are at rest. 达到静电平衡时，所有自由电子都处于静止状态。,3 Conditions of Electrostatic Equilibrium The electric field is zero inside a conductor 导体内部任何一点处 的电场强度为零,Corollary 1 The conducing surface is an equipotential surface, and all points in the interior are at the same potential as the surface, 导体表面是等势面，导体是等势体 Corollary 2 The field at the surface of the conductor (and just outside) is perpendicular to the surface,Proving 1,No tangential component can exist。 导体表面附近电场强度垂直于等势面。,Proving 2,3 Distribution of Charge a) All of the charges is on the surface of the conductor,Prove：,b) The electric field on the surface of a conductor,Note:,The field at the surface of the conductor (and just outside),c) Distribution of Charge of Spherical Conductor,Restricting factors： the electric field is zero inside a conductor.,Conductor shell（腔） (1) No charge in a conductor shell a The electric field is zero inside inside conductor and shell 导体内、空腔内场强皆为零； b The conductor and shell are equipotential 导体、空腔为等势体； 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.,(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.,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,+,+,+,+,+,+,+,5 Electrostatic Screening 静电屏蔽 Electrostatic 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,B电荷受力总是为零。 The charge inside shell can be shielded 壳可以屏蔽内部,If the charge B is changed, the force on the charge A is changed too. B电荷变化，A电荷受力会变化。 The charge A outside shell can not be shielded 壳不能屏蔽外边电荷A,If 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。,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：O2 H2 CO2,2 Dielectrics and Dielectric Polarization,无极分子：（氢、甲烷、石蜡等）,有极分子：（水、有机玻璃等）,电介质,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。,- +,- +,- +,- +,- +,- +,- +,- +,- +,- +,- +,- +,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,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。 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,+ + + + + + + + + + +,- - - - - - - - - - -,3 The relationship between electric polarization and bound charge,4 Electric displacement Gausss law in medium,Electric displacement 电位移矢量,Relative permittivity 相对电容率,The field in medium 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,1 10-3 10-6 10-9 10-12 F mF F微 nF纳 pF皮,1 The capacitance of an Isolated Conductor,Unit： Farads 法拉,The radius of the earth R6370km,C=7.0810-4F,3 Capacitance Capacitor,Capacitance is a measure of amount of charge a conductor holds at a given potential difference 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,2 Capacitance of a Capacitor,Capacitor：It is consists of two conductor plates being very closed,（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,3 Combinations of Capacitors 电容器的联接,(1) Connected in Series 串联,(2) Connected in Parallel 并联,For capacitors connected in series the charge on each capacitor is the same.,Capacitors connected in Parallel have the same potential difference across their plate,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。,4 Calculating the Capacitance of a Capacitor,(1) A Parallel-plate Capacitor,The capacitance of a capacitor depends on the separation distance d, the area S and the permittivity,(2) A Spherical Capacitor,(3) A Cylindrical Capacitor,-,取高为h 圆柱形高斯面,Note： 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 spherical capacitor is a standard capacitor,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),(b) Q=CU = 7.110-1250=3.510-10 C,The magnitude of the charge of one electron is 1.610-19 C, so the number N of electrons that can be stored is,=7.1 10-12 F=7.1pF.,Ex2 A spherical capacitor consists of two thin concentric spherical shells of radii a 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.,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 arb, contains charge q so, by Gausss law, the electric field on this sphere has intensity E=,Using and substituting for E,return,1 Energy storage in a capacitor,Electric potential energy is related to the work down in moving a charge in an electric field. The amount of work done to assemble the charge is equal to the potential energy stored in the system.,For a parallel-plate capacitor: C Start : No charge; End : -Q,+Q. At a moment: -q, q,The work is equal to the total energy stored in the capacitor,4 The Energy of Electric field,The work done to move the charge dq from A to B,2 The density of electric field energy,The energy stored in a capacitor is in the form of electric potential energy. Where is the energy? Consider the specific example of a parallel-plate capacitor,It means that the energy is stored in the electric field.,Although this discussion refers to a parallel-plate capacitor, the concept of energy density is defined by the same equation for capacitors of any shape,Energy density: the energy per unit volume,For a capacitor of any shape, the energy stored,解1 用电场能量公式:,在r处取半径为r, r+dr的球壳,在球壳内电场能量:,解2 导体球电容公式:,例 求半径为R,带电为+Q的导体球所具有的静电能.,问题 带电平行板电容器充满均匀介质,中间挖去一扁平的圆柱, A点和B点的D 和E谁大?,答案:EAEB DA=DB,return,5 Application,例1 无限长均匀带电圆柱面内外的场强分布： 0 ，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