Explanation

(b) Capacity of spherical conductor of $20\ cm$ diameter
$C_{1} = 4\pi\varepsilon_{0}r = 4\pi\varepsilon_{0} \times 10 \times 10^{- 2}$
Capacity of parallel plate air capacitor
$C_{2} = \frac{\varepsilon_{0}A}{d} = \frac{\varepsilon_{0}\lbrack\pi(2)^{2}\rbrack \times 10^{- 4}}{d} = \frac{\varepsilon_{0} \times 4\pi \times 10^{- 4}}{d}$
Hence $C_{1} = C_{2} \Rightarrow 40\pi\varepsilon_{0} \times 10 \times 10^{- 2} = \frac{40\pi\varepsilon_{0} \times 10^{- 4}}{4}$
$\Rightarrow d = 10^{- 3}m$