Deriving the method of images for conductors
Classical Physics
2010-12-08 v1
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.
Cite
@article{arxiv.1012.1369,
title = {Deriving the method of images for conductors},
author = {Chyi-Lung Lin and Hsien-Yi Lin},
journal= {arXiv preprint arXiv:1012.1369},
year = {2010}
}