大学物理教案设计之电通量与高斯定理.pdf

中国地质大学（武汉）大学物理教案设计课题:电通量高斯定理学院：班号：姓名：指导老师：课题：电通量 高斯定理课时：1教 学 目 标：1.理解电通量的概念2.掌握各种几何面电通量的计算3.通过典型例题分析，能自行导出高斯定理4.掌握高斯定理的含义，并能简单运用教 学 内 容：1.电通量指电场线对于某几何面的通过量值，对电通量概念的理解是导出高斯定理的前提与基础。2.高斯定理是静电学部分非常重要的定理之一，是计算具有高度对称性静电场的强大理论工具。3.高斯定理表明了场强通过任意闭合曲面的通量与闭合曲面内的电荷之间的数值关系，对高斯定理内容的正确理解是准确运用高斯定理的保证。教 学 重 点：高 斯定理的理解与运用教 学 难 点：利 用 高斯定理计算电场强度文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9教 学 过 程：复习回顾前面我们学习了库仑定律，我们知道了静止电荷周围存在静电场，并且用电场强度0FEq定量的描述电场的性质，还学习了电场的计算，由点电荷的电场3014qErr，采用叠加原理计算各种带电体的电场分布。本节我们课讨论电通量及高斯定理，对高斯定理的理解是本堂课的重点。为得出高斯定理，我们先引入电通量的概念。一、电通量1定义：通过电场中任一给定面的电场线的根数称为通过该面的电通量。用e表示。a.均匀电场通过垂直面的电通量：通过倾斜面的电通量：平面S的法线方向可以任意取定，一般确保0eb.非均匀电场如图所示，在 S上取面元dS，dS可看成平面，dS上E可视为均匀，设dS单位法向向量为n，记为d S。d S与该处E夹角为，则通过dS电场强度通量与场强的关系为：SdEde或者edEdS通过曲面 S的电场强度通量为：seeSdEd在任意电场中通过封闭曲面的电场强度通量:板书重点：点电荷电场公式3014qErr板书重点：edEdScoseESE SSEEnESeESE S文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9Ex y z esE dS一般约定：闭合面S的法线方向n规定指向外侧，电场线出则0e，入则0e。例：在均匀电场中有一立方形的闭合面，如图，已知ibE，则通过该闭合面的电通量是多少？解：左右SESEe左右SESE-0e二、高斯定理1高斯定理是关于闭合曲面的电通量的定理。我们先讨论最简单的情况。如图所示，q为正点电荷，S为以+q为中心以任意r 为半径的球面，dS为球面上一面元。其电通量为：320044eqqdE dSrdSdSrr通过闭合曲面S的电场强度通量为：330044esssqqE dSr ndSrdSrr2200044ssqqqdSdSrr2.点电荷电场中任意闭合曲面的电通量下面证明0eq对包围q的任意曲面也成立：q在 S内情形如图所示，在 S内做一个以q为中心，任意半径 r 的闭合球面 S1，由 1 知，通过 S1的电通量为0q。通过 S1的电力线必通过 S，说明为什么立方形的前后上下e=0课堂说明：该例题从侧面验证了高斯定理的正确性，但非严格的证明。e1eqS1SrqqEndSr文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9即此时1eses则通过 S的电场强度通量为：01eSE dSqq在 S外情形。如图，此时进入 S面内的电力线必穿出S面，即穿入与穿出 S面的电力线数相等，0esE dS结论：S外电荷对e无贡献00 eqSqqS在 内在 外3.点电荷系电场中闭合曲面的电通量在点电荷nqqqq,321电场中，任一点场强为：nEEEEE321通过某一闭合曲面电场强度通量为：snseSdEEEESdE321123nssssEdSEdSEdSEdS01iSq内即01eiSsE dSq内上式表示：在真空中通过任意闭合曲面的电通量等于该曲面所包围的一切电荷的代数和除以0。这就是真空中的高斯定理。高斯定理中的闭合曲面称为高斯面。对高斯定理的理解：以上是通过用闭合曲面的电通量概念来说明高斯定理，仅是为了便于理解而用的一种形象解释，不是严格的证明。高斯定理是在库仑定律基础上得到的，但是前者适用范围比后者更广泛。后者只适用于真空中的静电场，而前者适用于静电场和随时间变化的场，高斯定理是电磁理论的基本方程之一。用电场线“穿过”闭合曲面的方法来讨论电通量，可以看出电场线的描述问题的方便之处此公式的推导是重点点电荷系电场中的高斯定理区分内外电荷，进行详细分析证明。课堂要求：对高斯定理的理解是本节的重点和难点q文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9R高斯定理01eiSsE dSq内说明与 S内电荷有关而与 S 外电荷无关。但E是由 S内、外所有电荷共同产生的。电荷求和iq 指电荷带正负号求代数和，对于连续带电体则写成dqq高斯面是为了利用高斯定理而作的辅助面，可由我们任选。例：均匀带电球体球半径为R，体电荷密度为。求场强分布。解：电场分布也应有球对称性，方向沿径向。作同心且半径为 r 的高斯面，其电通量为：esE dS24Er01iSq内204qEr1.rR时，34qd Vr30Er32.rR时，34qR332013REr综上，0320rrR3ER1rR3r小结电通量：通过电场中某一曲面的电场线的数目高斯定理：电通量与场源电荷的关系课后思考无限长均匀带电圆柱面，半径为R，电荷面密度为0，求柱面内外任一点场强。板书重点：高斯定理公式esE dS01iSq内通过此例题了解高斯定理的简单应用，体会合理运用高斯定理在解决实际问题时能化繁为简照板书内容进行内容总结，本节重点在高斯定理的理解和运用文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9文档编码:CX1L5V10Z1Z1 HM5Q8E8H6F1 ZH9G7X4E5K9