NONUNIFORM Vol. Charge Density - V at the center of sphere

[JamesTheBond]

This should be easy, but for some odd reason I am not getting the right answer.

Assuming the potential V=0 at infinity, what is the V at the center of a sphere with volume charge density rho(r) = rho_0 * R/r

I keep getting (integral from 0 to R K*(4*pi*rho_0)*R/2) which I don't think is right.

Does anyone have any hints which will help me out here?

 

[Dick]

Your integrand is constant? That's not good. Unfortunately you didn't post enough of your work for me to have any idea of where you are going wrong. I think you want to use the homework form as well.

 

[JamesTheBond]

I did the problem again, now I have: V_0 = k*Q/R = k*4*pi*rho_0*R^2/2 = rho_0*R^2/(2*epsilon_0)

Can anyone confirm if I did this right?

 

[americanforest]

Try finding the spherical E in terms of charge density using Gauss's Law. Then integrate that in terms of dr from R to 0