Consider a cylindrical capacitor like that shown in Fig. Let d = rb - rc. be the spacing between the inner and outer conductors.
(a) Let the radii of the two conductors be only slightly different, so that d « ra . Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical. Capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of each cylinder. Use the result that in (1 + z) ≡z for |z|« 1.
(b) Even though the earth is essentially spherical, its surface appears flat to us because its radius is so large. Use this idea to explain why the result of part (a) makes sense from a purely geometrical standpoint.