1. The problem statement, all variables and given/known For a a uniformly charged sphere of radius R with total charge Q, show that the potential energy of a point charge q' varies with r U(r) = Qq'/4[tex]\pi[/tex][tex]\epsilon[/tex]R * (3/2 - r2/2R2 if r < R 2. Relevant equations [tex]\Delta[/tex]U = - [tex]\int[/tex]E(r)q'dr cos[tex]\theta[/tex] 3. The attempt at a solution I used that the electric field of q' when r < R is Qr/4[tex]\pi[/tex][tex]\epsilon[/tex]R3. I tried to integrate from initial to final for r, but then I only get 1/2 as opposed to 3. I have no idea where the 3 comes from. Can someone help please?