- #1

David0709

- 7

- 0

## Homework Statement

(i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate.

- (a) Find the electric field inside and outside of the sphere
- (b) Find and plot the electric potential inside and outside of the sphere

## Homework Equations

[/B]

E=−∇V

E = KQ1Q2/r^2

V = KQ1Q2/R

## The Attempt at a Solution

For part a) Field inside the sphere = r^2 / 4

*ε*0Outside the sphere R^4 / 4

*ε*0r^2With regards to part b)

I am aware that E=−∇V

So applying this formula we have:

Outside sphere:

R^4 /4

Inside sphere potential

-r^3 /12

*ε*0 rInside sphere potential

-r^3 /12

However when we let R = r we see these two equations for potential do not agree suggesting something (am not sure what ) is wrong.

Any help would be appreciated*ε*0However when we let R = r we see these two equations for potential do not agree suggesting something (am not sure what ) is wrong.

Any help would be appreciated