金属球与无限大导体平板系统电容的精确计算

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

用镜象法求解金属球与无限大导体平板系统的电容。根据数学物理理论,通过配置镜象电荷系列进行求解电容,即在金属球与无限大导体平板系统中配置镜象电荷系列,通过引入叠加系数Cn,2k可以精确确定镜象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。

The capacitance of a metal ball and an infinitely big conductor plane system is sought out by the method of electrical images. According to the theory of mathematic physics, the above-mentioned capacitance may be gained by means of deploying the series of electric charge images, that is deploying the series of electric charge image in a metal ball and an infinitely big conductor plane system and introducing superposition coefficient Cn,2k ,it is able to fix accurately on the positions and the charges of arbitrary electric charge image of the series, and use mathematic software MATLAB to calculate and construct the scheme, the capacitance can be accurately fixed on. This method is provided with the characteristic of intuition, simply and high precision calculation.