Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sph

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1. Electric Charges and Fields

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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

$\frac{{{n^2}}}{{n - 1}}$

B

$\frac{n}{{n - 1}}$

C

$\frac{2n}{{n + 1}}$

D

$\frac{{2n + 1}}{{n + 1}}$

Solution

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 $n C=\frac{4 \pi \epsilon_{o} a b}{b-a}$

$\therefore n C=\frac{C b}{b-a}$

Or $n b-n a=b$

$\operatorname{Or}(n-1) b=n a$

$\Longrightarrow \frac{b}{a}=\frac{n}{n-1}$

Standard 12

Physics

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