As shown in Figure 20.70, a spherical metal shell of radius r1 has a charge Q (on its outer surface) and is surrounded by a concentric spherical metal shell of radius r2 which has a charge −Q (on its...

As shown in Figure 20.70, a spherical metal shell of radius r1 has a charge Q (on its outer surface) and is surrounded by a

concentric spherical metal shell of radius r2 which has a charge −Q (on its inner surface).

(a) Use the definition of capacitance: to find the capacitance of this spherical capacitor.

(b) If the radii of the spherical shells r1 and r2 are large and nearly equal to each other, show that C can be written as

ε0A/s (which is also the formula for the capacitance of a parallel-plate capacitor) where A = 4πr2 is the surface area

of one of the spheres, and s is the small gap distance between them (r2 = r1 + s).