(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using integration by volume calculate the potential energy of a uniformly-charged sphere with total charge Q. I assume the sphere is solid with uniform charge density.

2. Relevant equations

U=(1/8pi)*∫(E^2)dV

3. The attempt at a solution

My problem is that when I attempt to integrate from 0 to r, the 1/r^2 term of E blows up at 0 and I'm left with infinite potential energy. Is there another equation I can integrate? Which integral should I be taking to evaluate this problem, or what limits should I be using?

I'm trying to build up the total E-field layer-by-layer, by adding the E-fields of multiple overlapping spheres, but I still can't get the integral.

Edit: Nevermind I've got it. U=(3/5)*(Q^2/r)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calculate the potential energy of a uniformly-charged sphere

**Physics Forums | Science Articles, Homework Help, Discussion**