球面镜像电荷的一种求解方法

A New Derivation of Spherical Mirror Charge

对电磁场教学中的镜像法进行了研究,给出了一种球面镜像法中镜像电荷位置及大小的求解方法。依据唯一性定理,以镜像电荷为未知量,利用理想导体电位条件,在三维空间建立待定系数方程,推导出镜像电荷的大小和位置。从三维空间出发的推导与常用教材中利用对称性的二维推导相比更具一般性,可以用于课程中的探究式教学或课程实践教学环节,在电磁场课程教学中有较好的参考价值,可为教学者和学习者提供有益的参考。

This paper presents a method to solve the position and quantity of mirror charge in spherical mirror method.According to the uniqueness theorem,parameters of the mirror charge are taken as the unknown quantities,and by using the ideal conductor point condition,the undetermined coefficient equation in three-dimensional space is established,and the quantity and position of the mirror charge are derived.The derivation given in this paper is more general than the content of common textbooks,and can be used in inquiry-based teaching or course practice teaching.The derivation has a good reference value in the teaching of electromagnetic field theory courses and can provide a useful reference for teachers and students..