Deriving the method of images for conductors

Abstract

We start from the simple fact that the method of images can always be used to obtain {\Phi}_{\sigma} (r^\to_in), which is the potential inside conductor produced by induced surface charges. We use this fact to construct image method for outside potential {\Phi}_{\sigma} (r^\to_out). We show that if we can find a relation between {\Phi}_{\sigma} (r^\to_out) and {\Phi}_{\sigma} (r^\to_in), then the image method for {\Phi}_{\sigma} (r^\to_in) can be used to derive the image method for {\Phi}_{\sigma} (r^\toout). The number, the position and the amount of charge of the images can be directly derived. The discussion can be extended to the general n dimensions.