Question

(10%) Problem 8: A spherical capacitor consists of a single conducting sphere of radius R = 12 cm that carries a positive charge Q = 65 nC. The capacitance for this spherical capacitor is given by the equation C-4jEjR 14% Part (a) Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor Write your cqu ation in terms of R, Q, and eg Grade Summarv Deduction:s Potential 0% 100% 7 8 9 Submissions Attempts remaining: 3 (4% per attempt) detailed view 0 END DELCLEAR Submit Hint Hits: 3% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback. 14% Part (b) Use Gauss's Law to write an equation for the electric field everywhere inside the spherical capacitor (r < R) 14% Part (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 є0 14% Part (d) Write an equation for the energy density due to the electric field outside the spherical capacitor in terms of Q, r, and EO 14% Part (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 cncrgy contained in the shell in terms of Q, r, dr, and E) elà 14% Part (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 e) 14% Part (g) Calculate the energy stored in the capacitor in units of microoules