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

  • #1
JamesTheBond
18
0
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

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
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.
 
  • #3
JamesTheBond
18
0
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?
 
  • #4
americanforest
223
0
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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