A spherical capacitor consists of a single conducting sphere of radius R = 14 cm that carries a positive charge Q = 35 nC. The capacitance for this spherical capacitor is given by the equation C = 4Πε0R.
(a) Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor. Write your equation in terms of R, Q, and ε0.
(b) Use Gauss's Law to write an equation for the electric field everywhere inside the spherical capacitor (r < R).
(c) Use Gauss's Law to write an equation for the radial electric field at a radius r outside the spherical capacitor. Give your answer in terms of Q, r, and ε0.
(d) Write an equation for the energy density due to the electric field outside the spherical capacitor in terms of Q, r, and ε0.
(e) Consider a thin spherical shell of thickness dr and radius r > R that is concentric with the spherical capacitor. Write an equation for the total energy contained in the shell in terms of Q, r, dr, and ε0.
(f) Find the total energy stored in the field by integrating the energy over the radius outside the conducting shell. Write this total energy contained in the shell in terms of Q, R, and ε0.
(g) Calculate the energy stored in the capacitor in units of microjoules. (please give all the steps and answers?