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

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Homework Help Overview

The discussion revolves around calculating the electric potential at the center of a sphere with a non-uniform volume charge density defined as ρ(r) = ρ₀ * R/r. Participants are exploring the implications of this charge distribution on the potential, assuming V=0 at infinity.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining the integration process for calculating the potential and questioning the correctness of their integrands. There is a focus on the application of Gauss's Law and the relationship between charge density and electric field.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and seeking confirmation on their approaches. Some guidance has been offered regarding the use of Gauss's Law and the need for a proper setup of the integral.

Contextual Notes

There is a noted lack of sufficient detail in some posts, which may hinder the ability to fully assess the reasoning and calculations presented. Participants are encouraged to provide more context for their work.

JamesTheBond
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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?
 
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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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