A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, `rho=rho_(0)r/R`, where `rho_(0)` is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is `Q=pirho_(0)R^(3)` (ii) the electric field inside the sphere has a magnitude given by, `E=(KQr^(2))/R^(4)`

Answer

(a) `vec(E)=(rho_(0) r^(2))/(4 epsi_(0)) hat(r); V=(rho_(0) [4R^(3)-r^(3)])/(12 epsi_(0))` (b) `vec(E)=(rho_(0)R^(4))/(4epsi_(0) r^(2)) hat(r); V=(rho_(0)R^(4))/(4epsi_(0)r)`