静电场中的镜像法与分离变量法

静电场中得镜像法与分离变量法 摘要:静电场得基本问题就是求解给定边界条件下得泊松方程或拉普拉斯方 程得解,本文分别阐述在求解区域内有与没有自由电荷分布得情况下,应用镜像法与分离变量法求解;同时,举例来演示应用镜像法与分离变量法得解题思路、步骤与结果讨论以及一些注意点,并在相同情况下分别应用镜像法与分离变量法进行对比讨论;深化理解镜像法与分离变量法及其特征。 关键词:静电场、镜像法、分离变量法。 The Method of Mirror Image and the Separate Variational Method in the Electrostatic Field Abstract: The basic problem of electrostatic field is to explore the solution of Poisson equation or Laplace equation under its given boundary condition 、 This article respectively explains the approaches to explore the solution using mirror image and separate variational methods under the tobeexplore solution area situation which has and which lacks freedom electric charge distribution 、 Meanwhile, it takes some instances to demonstrate the problemsolving thoughts and steps applying mirror image and separate variational methods 、 It also provides some discussions about the result and the points needing to be noted in the process of this demonstration 、 This writer also tries to help the readers to deeply understand the methods of mirror image and separate variational methods and their characteristics by doing contrast discussion under the same condition 、 Keywords: the electrostatic field, the method of mirror image, the separate variational method、 1、引言:静电场与电源外恒定电场得边值问题得求解,可归纳为在给定 边界条件下,对拉普拉斯方程或泊松方程得求解。很多文章已经就界面形状就是比较简单得几何曲面得这类问题给出了解析形式得求解,这种解析形式求解得常用方法分别就是镜像法与分离变量法。本文在应用此方法求解边值问题得探讨基础上,进一步地就镜像法与分离变量法得应用进行对比与讨论。 2、静电场中得静像法与分离变量法得介绍 i)、镜像法 拉普拉斯...