1. The problem statement, all variables and given/known data Using the definition of electric potential as well as the electric field energy definition of potential energy, determine the electric potential of a uniformly charged spherical shell of radius R. 2. Relevant equations I know that V= -∫E.dl as we take dl from infinity to R. Also, I just learned how U=∫(1/2)*ε*E^2 dV, where we integrate over all space. 3. The attempt at a solution From the first definition of potential, I can easily plug in E=Q/(4*∏*ε*R^2) and integrate to get V=Q/(4*∏*ε*R), which I obviously know to be the correct potential of the sphere. Now, my problem with the second definition is that in finding U for the sphere, I get to the integral (1/2)*ε*Q^2/(16*π^2*ε^2) ∫ (1/r^2)*4*π*r^2 dr, where r is integrated from R to infinity (because E=0 inside the shell). When I evaluate this, I get Q^2/(8*π*ε*R), which is half of what I want... I don't get what's going wrong!