Problem 3.216

A parallel-plate air capacitor whose plates are separated by a distance $d=5.0 \mathrm{~mm}$ is first charged to a potential difference $V=90 \mathrm{~V}$ and then disconnected from a dc voltage source. Find the time interval during which the voltage across the capacitor decreases by $\eta=1.0 \%,$ taking into account that the average number of ion pairs formed in air under standard conditions per unit volume per unit time is equal to $\dot{n}_{i}=5.0 \mathrm{~cm}^{-3} \cdot \mathrm{s}^{-1}$ and that the given voltage corresponds to the saturation current.