A cylindrical shell of radius r2 and infinite extent in z encloses a second cylindrical
shell of radius r1 < r2. Both shells share a common z axis. The inner shell carries total charge -q per length L while the outer shell carries total charge +q per length L.
(a) Find the total E field from a length L of the infinite coaxial cylindrical shells using Gauss’s law. Write the E field separately for r < r1, r1 < r < r2, and r > r2.
(b) Using this expression for E, find the energy of this configuration for a given length L by integrating the square of the E field over all space.
(c) Now find the total E field of each shell separately, express E2^2 = E1^2+E2^2+E1.E2 and show that integrating this expression instead gives the same answer as in part (b).