Q106 / 180 · AIIMS 2014 · Physics

The diameter of the plate of a parallel plate condenser is $6 \mathrm{~cm}$. If its capacity is equal to that of a sphere of diameter $200 \mathrm{~cm}$, the separation between the plates of the condenser is

A
$4.5 \times 10^{-4} \mathrm{~m}$
Correct answer
B
$2.25 \times 10^{-4} \mathrm{~m}$
C
$6.75 \times 10^{-4} \mathrm{~m}$
D
$9 \times 10^{-4} \mathrm{~m}$

Solution

As $\frac{\varepsilon_0 A}{d}=4 \pi \varepsilon_0 R$ $d=\frac{A}{4 \pi R}=\frac{\pi(6 / 2)^2}{4 \pi(100)}=2.25 \times 10^{-2} \mathrm{~cm}$ $=2.25 \times 10^{-4} \mathrm{~m}$

Hence, the correct answer is option: 'B'.

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