The diameter of each plate of an air capacitor is 4 cm . To make the capacity of this plate capacitor equal to that of $20 \mathrm{cm}$ diameter sphere, the distance between the plates will be
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Capacity of spherical conductor of 20 cm diameter $C_1 = 4 \pi \varepsilon_0 r = 4 \pi \varepsilon_0 \times 10$
Capacity of parallel plate air capacitor
$C_2 = \frac{\varepsilon_0 A}{d} = \frac{\varepsilon_0 [\pi (2)^2]}{d} = \frac{\varepsilon_0 \times 4 \pi}{d}$
Hence $C_1 = C_2$ ⇒ ⇒ $4\pi \varepsilon_0 = \frac{4\pi \varepsilon_0}{d}$ ⇒ ⇒ $d = 10^{-3} m$
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