A solid conducting sphere of radius R carries a charge Q. Calculate the electric-field energy density at a point a distance r from the center of the sphere for
(a) r < R and
(b) r > R.
(c) Calculate the total electric-field energy associated with the charged sphere.
(d) Explain why the result of part (c) can be interpreted as the amount of work required to assemble the charge Q on the sphere.
(e) By using Eq. (24.9) and the result of part (c), show that the capacitance of the sphere is as given in Problem 24.67.