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The radius of the circular plates of a parallel plate capacitor is R₁, with air as dielectric. The distance between the plates if the capacitance is equal to that of an isolated sphere of radius ‘R₂’ is

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$\frac{R_{1}^{2}}{4 R_{2}}$

$\frac{R_{1}^{2}}{R_{2}}$

$\frac{R_{1}}{R_{2}}$

$\frac{R_{1}^{2}}{4}$

answer is A.

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Detailed Solution

$C_{1} = \frac{\in_{0} {πR}_{1}^{2}}{d} C_{2} = 4 π \in_{0} R_{2} Given, C_{1} = C_{2} \Rightarrow \frac{\in_{0} {πR}_{1}^{2}}{d} = 4 π \in_{0} R_{2} \Rightarrow \frac{R_{1}^{2}}{d} = 4 R_{2} \Rightarrow d = \frac{R_{1}^{2}}{4 R_{2}}$

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