I have a question,it's not homework related..I know the electro-static energy of a sphere is:(3/5)kQ/R
I tried to calculate it today using the expression:
U = 1/2 * integral (phi * rho dV)
where: phi is the potential, rho is charge density(uniform), dV is the volume element.
it's not hard to calculate the potential everywhere in space,but my problem is when I integrate over volume elements (4*pi*r^2 dr) should I integrate over:
r=0 to r=infinity? it doesnt seem reasonable because rho=0 outside the sphere.
anyway I tried to do that,i.e integrating over r=0 to r=R using the potential inside the sphere,but I didnt get the correct answer.
I would love to get some help with this.