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Assuming ab expression for the potential...

Assuming ab expression for the potential of an isolated conductor, show that the capacitance of such a sphere will be increased by a factor n, if it is enclosed within an earthed concentric sphere, the ration of the spheres being `n(n - 1)`.

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The capacitanace of an isloated conducting sphere of radius a is `C = 4pi in_(0) a`
When surrounded by an earthed sphere of radius b, its capacitance becomes
`C' = 4pi in_(0) (ab)/(a-b)`
`(C')/(C ) = (ab)/(a(b-a)) = (b)/(b-a) = (1)/(1- (a)/(b)) = (1)/(1 - (n -1)/(n)) = n`
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