Deriving the method of images for conductors

We start from the simple fact that the method of images can always be used to obtain Φ_σ (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 Φ_σ (r^\to_out). We show that if we can find a relation between Φ_σ (r^\to_out) and Φ_σ (r^\to_in), then the image method for Φ_σ (r^\to_in) can be used to derive the image method for Φ_σ (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.

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