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2. Electric Potential and Capacitance
medium
The capacitance $(C)$ for an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0a$. If the sphere is enclosed with an earthed concentric sphere. The ratio of the radii of the spheres $\frac{n}{{(n - 1)}}$ being then the capacitance of such a sphere will be increased by a factor
A
$n$
B
$\frac{n}{{(n - 1)}}$
C
$\frac{{(n - 1)}}{n}$
D
$a \cdot n$
Solution
Capacity of an insulated spherical capacitor of radius $b$ is $4 \pi \epsilon_{0} b$ where there is a system of two shell with outer shell being earthed, the system behaves as a capacitor with capacitance,
$C=4 \pi \epsilon_{0}\left(\frac{a b}{a-b}\right)=n .4 \pi \epsilon_{0}$
$\left(\frac{a}{a-b}\right)=n$
Standard 12
Physics
