A non-uniform but spherically symmetric distribution of charge has a charge density P(r) given by
p(r)=p_0 ( 1-r/R) for r < or = R
p(r)=0 for r > or = R
where
p_0 =3Q/(piR^3)
is a positive constant.
a) Show that the total charge contained in the charge distribution is Q
b) Show that the electric field in the region r = R is identical to that produced by a point charge Q at r = 0.