What distance should the two plates each of area $2 * 10^2 \;m^2$ of an air capacitor be placed in order to have the same capacitance as a spherical conductor of radius $0.5\;m$?

Given,
Area $(A) = 2 \; * \; 10^{2}\;m^2$
Radius $(R) = 0.5\;m$
Distance $(d) = ?$

For two plate capacitor,

$C = \frac{\epsilon_0\;A}{d}$ .......... (i)

For Spherical conductor,

$C = 4 \; \pi \; \epsilon_0 \; R$ .......... (ii)

According to question, if both of them have same capacitor, then from the equation $(i)$ and $(ii)$, we get

$d =$ $ \frac{A}{4\; \pi \; R} = \frac{2 \; * \; 10^{2}}{4 \; *\; \pi \; * 0.5} $ $= 15.92\;m$

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