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]]>The basic idea is a point outside the circle will match up with a point inside the circle, and that their distances will be reciprocals of each other.

*screeching, sound of car crash in Dan’s head*

You’ll have to walk through that one a little slower for me some time.

]]>There’s a whole method in physics for finding the electric potential due to a collection of charges near a conducting surface where you imagine the image of the charges reflected across the surface, then compute the potential of the two sets of charges ignoring the surface. Turns out this gives the correct potential and is much easier than figuring out exactly what happens on the surface of the real conductor.

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