金属球与无限大导体平板系统电容的研究与计算  

Accurate Calculation of the Capacitance of the System for a Metal Ball and An Infinitely Big Conductor Plane

作　　者：胡文江[1] 胡先权[2] 

机构地区：[1]重庆邮电大学通信与信息工程学院,重庆400065 [2]重庆师范大学物理学与信息技术学院,重庆400047

出　　处：《山西师范大学学报（自然科学版）》2007年第3期54-58,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：重庆市科委自然科学基金项目(2005BB8267);重庆市教育基础理论研究基金(KJ060813)

摘　　要：采用镜像法与叠加系数法求解了金属球与无限大导体平板系统的电容.根据数学物理理论,本文通过引入叠加系数Cn,k的方法,在金属球与无限大导体平板系统中配置镜像电荷系列,可以精确确定镜像电荷系列中任意象电荷的位置和电量,并采用计算技术工具软件Matlab进行运算与作图,精确计算系统的电容.这种方法分析过程直观、简捷、计算精度高等特点.The capacitance of the system for a metal hall and an infinitely big conductor plane is sought out by the method of electrical images. According to the theory of mathematic physics, above-mentioned the capacitance may be gained by means of deploying the series of electric charge image, that is deploying the series of e- lectric charge image in the system for a metal hall and an infinitely big conductor plane and introducing superposition coefficient, it is able to accurately fix on the positions and the charges of arbitrary electric charge image of the series, and use mathematic software Matlah to calculate and construct the scheme, the capacitance can he accurately fixed on. This method is provided with the characteristic of intuition, simply and high precision calculation.

关 键 词：镜像法 镜像电荷 电容 泊松方程 

分 类 号：O441.1[理学—电磁学] O411.1[理学—物理]