1. Given a sphere of uniform charge Q, radius R: Find an expression for the electrostatic potential V as a function of r for r ≤ R. Prior proof: E= Q(r)/(4πϵ0)r^2 ,for r≤R where Q(r) is the excess charge in the spherical volume of radius r 2. Relevant equation: V = Q/(4πϵ0)r 3. I tried integrating for spheres of radius ri over 0 - R where ∆Qi is each small bit of charge and ∆Qi = (Q/V)∆Vi giving (3Qr2/R3)∆r. My eventual answer resulted in (Q/4πϵ0)(R3 - r3) I know there's some form of integral involved, but i'm not sure what/where. The answer (shown on the answers) is shown to be V (r) = [Q/(8πϵ0R3)](3R2 - r2) but no working is provided, and I can't for the life of me figure out what they did. Thanks.