Chapter 25, Problem 40AP

(a) Two spheres have radii a and b, and their centers are a distance d apart. Show that the capacitance of this system is

$C=\frac{4\pi {ϵ}_0}{\frac{1}{a}+\frac{1}{b}-\frac{2}{d}}$

provided d is large compared with a and b. Suggestion: Because the spheres are far apart, assume the potential of each equals the sum of the potentials due to each sphere. (b) Show that as d approaches infinity, the above result reduces to that of two spherical capacitors in series.