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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
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B
n2n1
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C
2nn+1
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D
2n+1n+1
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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    $$(n-1)b = na$$
$$\implies \ \dfrac{b}{a} = \dfrac{n}{n-1}$$

Physics
NCERT
Standard XII

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