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

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 dont think is right.

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

Answers and Replies

Dick
Science Advisor
Homework Helper
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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.
 
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?
 
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
 

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