Problem 3.218

The gas between the capacitor plates separated by a distance \(d\) is uniformly ionized by ultraviolet radiation so that \(n_{i}\) electrons per unit volume per second are formed. These electrons moving in the electric field of the capacitor ionize gas molecules, each electron producing \(\alpha\) new electrons (and ions) per unit length of its path. Neglecting the ionization by ions, find the electronic current density at the plate possessing a higher potential.