球域静电问题是电动力学教学的经典问题并广泛应用于工程技术中.开尔文首创的电像法，成为此类问题的重要工具.本文系统研究了球形边界的格林函数，针对狄利克雷、诺伊曼与罗宾三类边界条件，分别给出了球内外的格林函数解析解与镜像源构型.对于诺伊曼与罗宾边界，本文基于自由空间格林函数，通过勒让德多项式展开添加边界修正项，经积分得到闭式解，揭示出这两种边界条件下，诺伊曼线上的镜像源分别表现为均匀分布与幂律分布的射线或线段形式.

Electrostatic problems in spherical domains are classical problems in electrodynamics and are widely applied in engineering and technology. The method of images, pioneered by Kelvin, has become a central tool for such problems. This paper systematically studies Green’s functions for spherical boundaries. For three types of boundary conditions—Dirichlet, Neumann, and Robin—this paper derives the analytical solutions of Green’s functions both inside and outside the sphere, along with their corresponding image source configurations. For Neumann and Robin boundaries, the research starts from the freespace Green’s function. Legendre polynomial expansions are employed to introduce boundary correction terms. Closedform solutions are obtained through integration. The results show that under these two boundary conditions, the image sources on the Neumann line appear as a uniform and a powerlaw distribution of rays or line segments, respectively.