A charge Q is spherically symmetrically distributed over a non$-$conducting sphere of radius R$.$ Inside the sphere the electric field E is constant.

$($a$)$ Write the expression for the space charge density $\backslash$rho as a function of the distance r from the center of the sphere.

$($b$)$ Calculate the electric potential V inside and outside the sphere.

$($c$)$ Graph E$,$ V$,$ and $$rho as a function of r$$