(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 =  4?ε0 1 a +  1 b −  2 d  provided that 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.

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(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 = 
4?ε0
1
a
 + 
1
b
 − 
2
d
 
provided that d is large compared with a and bSuggestion: 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.
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