The plate spacing in a typical parallel-plate capacitor is about \(50 \mu \mathrm{m}\).

(a) What is the plate area in a \(1-\mu \mathrm{F}\) capacitor?

(b) Given that the electric field at which electrical breakdown occurs in air is about \(3 \times 10^{6} \mathrm{~V} / \mathrm{m}\), what is the maximum charge that this capacitor can hold?

(c) How many electrons does this charge correspond to? (The electron's charge is \(e=1.6 \times 10^{-19} \mathrm{C}\).)