关键词: 电像法, 分离变量法, 格林函数 

Abstract: It is an interesting problem to investigate the electrostatic field between two intersecting planes with given opening angle and charge distribution. For simplicity, we focus on the case that the source is a point charge. First, the potential distribution of some special opening angles is analyzed by using the method of image. Furthermore, the general case is solved by applying the separation of variables. The equivalence of the two results is verified by mathematical derivations. Finally, the discussion is generalized to Neumann and mixed boundary conditions, where the general solutions of electric potential and a series of identities for the second kind of Legendre function are obtained.

Key words: method of image, separation of variables, Green function