1. The problem statement, all variables and given/known data A point charge q is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. How much work would it take to move the point charge out to infinity (through a tiny hole drilled in the shell)? [answer: q2/8πε0)(1/a - 1/b) 2. Relevant equations W = ε0/2 ∫E2 dτ W = 1/2 ∫ρV dτ 3. The attempt at a solution Since the point charge induces a uniform charge of -q on the inner surface and q on the outer surface, I figured I could figure out the total energy of this system and then this would be how much energy you get back when dismantling it by taking q out infinitely far away. So I figured it takes zero work to initially move the point charge and then I calculated the energies of the two induced surface charges using the second integral above but I get W = q2/8πε0 (1/a +1/b). What' wrong here?