A total charge Q is distributed uniformly throughout a spherical volume of radius R. Let r denote the distance of a point from the center of the sphere of charge. Use Gauss's law to derive an expression for the magnitude of the electric field at a point

a. outside the sphere, r > R;
b. inside the sphere, r < R.
The electrostatic potential is assumed to be zero at an infinite distance from the sphere.
c. What is the potential at the surface of the sphere?
d. Determine the potential at the center of the sphere.