利用镜像法求解劈形导体边界的讨论

Discussion on solving the boundary of wedge conductor by image method

镜像法是解析求解高对称性静电场边值问题的一种简便方法.本文研究劈形边界导电系统的镜像问题,此时导电劈的夹角α存在附加条件α=π/n(n=2,3,4,...),该附加条件是教学过程中学生的疑问点.镜像法求解静电问题的理论依据是唯一性定理,在保持边界条件与边值关系不变的原则下,推导导电劈夹角α的数学表述并解释分析其存在附加条件的原因.

The method of images is an easy way to solve the problem of high symmetry electrostatic field boundary value problem.In this paper,the mirroring problem of the wedge boundary conductive system is studied,at this time there are additional conditions in the angle of the conductive wedgeα=π/n(n=2,3,4,…),which is the question point of students in the teaching process.The theoretical basis for solving the electrostatic field by the method of images is the unique theorem,and under the principle of keeping the relationship between boundary condition and edge value unchanged,the mathematical expression of conductive wedge angle is deduced and the reasons for its additional conditions are explained.