(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
E = KQ1Q2/r^2
V = KQ1Q2/R
The Attempt at a Solution
For part a) Field inside the sphere = r^2 / 4ε0
Outside the sphere R^4 / 4ε0r^2
With regards to part b)
I am aware that E=−∇V
So applying this formula we have:
R^4 /4ε0 r
Inside sphere potential
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