The gas between the capacitor plates separated by a distance `d` is unifromly ionized by ultraviolet radiation so that `n_(1)` electrons per unit volume per second are formed. These electrons moving in the electric field of the capacitor ioinze gas molecules , each electrons producing `alpha` new electrons (and ion) per unti length of its path.Neglecting teh ionization by ions, find the electronic current density at the plate possessing a higher potential.

Explanation

Since the electrons are produced uniformly through the volume, the total current attaining saturation is clearly,
`I = int_(0)^(d) e(n_(i) A dx) e^(alpha x) = e dotn_(i) A ((e^(alpha d) - 1)/(alpha))`
Thus, `j = (I)/(A) = e dotn_(i) ((e^(alpha d) - 1)/(alpha))`