Question

[Key Concept: The dielectric strength fixes the minimum plate separation; at fixed capacitance this fixes the minimum plate area.]

$$\begin{matrix} & k = 2.5 \\ & E = 1.8 \times 10^{7} \\ & C = 72nF \\ & \text{ }V = 4000\text{ }V \\ & E = \frac{V}{\text{ }d} \\ & \text{ }d = \frac{4000}{1.8 \times 10^{7}} \end{matrix}$$

$$\begin{matrix} & \frac{k\epsilon_{0}\text{ }A}{\text{ }d} = 72 \times 10^{- 9} \\ & \frac{k4\pi\epsilon_{0}\text{ }A}{4\pi\text{ }d} = 72 \times 10^{- 9} \\ & \frac{2.5 \times A \times 1.8 \times 10^{7}}{9 \times 10^{9} \times 4\pi \times 4000} = 72 \times 10^{- 9} \\ & \frac{\pi{\text{ }d}^{2}}{4} = \frac{9 \times 4\pi \times 4 \times 4 \times 10^{- 3}}{2.5} \\ & \text{ }d = 96\text{ }cm \\ & \text{~option (d)~} \end{matrix}$$