That's an interesting question! I think the effect would be the opposite of what ChuckMcM imagines: as a (say) positively charged particle inside a positively charged conductive sphere moves from the center toward one side of the sphere, it repels the charges on that side more than it does on the opposite side. It does seem like that would cause those charges to spread out slightly, making that part of the sphere negative relative to the other side, accelerating the particle in the direction it was already going, until it hits the sphere. The minimum energy is thus where all charges within the sphere are on its surface; none are inside. I believe this is consistent with observation.
It has been an interesting conversation so far. Since I have been going through Jackson's text it makes a useful problem to work. I'm working up the field equations for inside the sphere, inside a charged concave surface, and inside a concave depression in a sphere. I suspect that this thread will be dead before I'm done but the next time around I'll be able to post a link to a paper :-).
Coming up with a closed-form solution would be beyond my mathematical abilities at this point, having not done any calculus to speak of in 40 years, but I'll be interested to see if you can.
