Question

# Capacity of an isolated sphere is increased $$n$$ times when it is enclosed by an earthed concentric sphere. The ratio of their radii is

A
nn1
B
n2n1
C
2nn+1
D
2n+1n+1

Solution

## The correct option is B $$\dfrac {n}{n - 1}$$Let the radius of isolated sphere be $$a$$ and that of earthed sphare be $$b$$.Capacitance of isolated sphere  $$C = 4\pi\epsilon_o a$$Capacitance of isolated sphere enclosed in earthed sphere  $$nC = \dfrac{4\pi\epsilon_o ab}{b-a}$$$$\therefore$$    $$nC = \dfrac{C \ b}{b-a}$$Or    $$nb - na = b$$Or    $$(n-1)b = na$$$$\implies \ \dfrac{b}{a} = \dfrac{n}{n-1}$$PhysicsNCERTStandard XII

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