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## Homework Statement:

- A thick spherical shell of charge Q and uniform volume charge density ρ is bounded by radii r1 and r2 > r1. With V = 0 at infinity, find the electric potential V as a function of distance r from the center of the distribution, considering regions (a) r > r2, (b) r2> r > r1 and (c) r < r1 (d) Do these solutions agree with each other at r = r2 and r = r1?

## Relevant Equations:

- NA

a. This solution is i can consider the charge Q as a point charge and the electric potential at a distance r is

## V = Q/(4πεοr)##

b. This is where the confusion starts again when r2>r>r1, my answer

##

V = ρ*4*π(r^3 - r_1^3)/(3*4πεοr) \\

V = ρ*(r^3-r_1^3)/3εοr; ##

I know i am making some mistake as the answer does not match.

c. For r < r1, the potential should be 0. I know that for a conducting sphere the potential at the surface is equal to at the center and they are equi- potential surfaces. But in this case below r1 there is no surface hence the potential should be 0. Please advise.

## V = Q/(4πεοr)##

b. This is where the confusion starts again when r2>r>r1, my answer

##

V = ρ*4*π(r^3 - r_1^3)/(3*4πεοr) \\

V = ρ*(r^3-r_1^3)/3εοr; ##

I know i am making some mistake as the answer does not match.

c. For r < r1, the potential should be 0. I know that for a conducting sphere the potential at the surface is equal to at the center and they are equi- potential surfaces. But in this case below r1 there is no surface hence the potential should be 0. Please advise.