Finding the energy of a charged sphere

[Eitan Levy]

Homework Statement

Let's say we have a charged sphere with a radius R and total charge Q with constant density over the sphere. Find the energy of the sphere.

Relevant Equations

V=KQ/R

In class we were taught that for spherical bodies we may use the formula below where the integral is done over the volume of the body. However, if we assume that the potential in infinity is 0, the potential inside the sphere is constant and equals KQ/R, where Q is the total charge of the sphere. If I try to do the integral from r=0 to r=R, while plugging the constant density Q/(4/3*pi*R^3)) and dV=4*pi*r^2*dr, I get a result of KQ^2/(2R). Online I can see it is not right.

What is the problem?

 

[TSny]

If the charge is spread uniformly throughout the volume of the sphere, then V is not constant inside the sphere.