A charge q is distributed uniformly throughout a non-conducting spherical volume of radius R.(a) Show that the potential at a distance x from the centre when x lt R is given by `V=(q(3R^(2)-x^(2)))/(8piepsilonR^(3))` and the self potential energy of the charge distributed is `U=(3q^(2))/(20piepsilonR).` [Hint: Calculate the potentials due to the charge inside the concentric sphere through the point and due to the charge in the outer portion and add. The calculate self potential energy first calculate the elementary work done in building the charge in shell of thckness dz over a sphere of radius z and then integrate from z=0 to z=R.]