Problem

1. (a) Two spheres have radii

a

and

b

and their centres are at a distance

d

apart. Show that the capacitance of this system is

C = \frac{4\pi\epsilon_0}{\frac{1}{a} + \frac{1}{b} \pm \frac{2}{d}}

provided that

d

is large compared with

a

and

b

. 2. (b) Show that as

d

approaches infinity the above result reduces to that of two isolated spheres in series. Note : In series,

\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}