The original question is
Two concentric metallic shell’s of radius R and 2R, out of which the inner shell is having charge Q and outer shell is uncharged. If they are connected with a conducting wire. Then what is the heat produced in the wire?
Well my idea is as soon as the wire is connected, it becomes a metallic shell. And the usual thing happens, all the charges move to the surface.
I calculate the change in potential of the shell in the two cases.
$\Delta U$=kQ/R-kQ/2R. We multiply it by the charge to get the change in potential energy. The answer should be $kQ^2/2R$. But the answer is half of that. I am missing some part of energy conservation. Surely not all of the change in potential energy gets converted to heat. Where does half of the change go then?