(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.
(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 | ||||||
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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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