一道双导体球静电感应题的引申与探究

Extension and analysis of a problem on double-conductor-sphere electrostatic induction

介绍了一道关于双导体球静电感应的题目及其解法,并从中引申出几个问题.基于镜像法的基本思想,设计出一种适用于求解任意多个带电导体球静电感应的镜像电荷构造方法,对上述问题进行数值求解,分别得到在对称情形和非对称情形下的空间电势和电场,绘制出导体球面上的电荷密度分布曲线,并讨论了其物理意义.

A problem on the electrostatic induction of double conductor spheres and its solution are presented,and several problems are derived from it.Based on the basic idea of the mirror method,a mirror-charge construction method is designed for solving the electrostatic induction of any multiple charged conductor spheres,and the above problems are solved numerically to obtain the spatial potential and electric field in the symmetric and asymmetric cases,respectively.The charge density distribution curves on the sphere of the conductor are plotted and their physical significance is discussed.