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Physics Question on Capacitors and Capacitance

The diameter of the plate of a parallel plate condenser is 6 cm6\,cm. If its capacity is equal to that of a sphere of diameter 200 cm200\, cm, the separation between the plates of the condenser is

A

4.5×10−4m4.5 \times 10^{-4} m

B

2.25×10−4m2.25 \times 10^{-4} m

C

6.75×10−4m6.75 \times 10^{-4} m

D

9×10−4m9 \times 10^{-4} m

Answer

2.25×10−4m2.25 \times 10^{-4} m

Explanation

Solution

Asε0Ad=4πε0RAs \frac{\varepsilon_{0}A}{d}=4\pi\varepsilon_{0}R d=A4πR=π(6/2)24π(100)=2.25×10−2cmd=\frac{A}{4\pi R}=\frac{\pi\left(6/2 \right)^{2}}{4\pi\left(100\right)}=2.25\times10^{-2} cm =2.25×10−4m= 2.25 \times 10^{-4} m