To account for the effect of space charge on the operation of a plane diode with an interelectrode distance d, it is necessary to establish the dependence of the charge density ρ, potential φ, and electron velocity v on the distance to the cathode x. The electron velocity and field strength at the cathode at currents far from saturation can be assumed to be zero. In the case when the cathode is grounded, the potential can be represented as φ = V (x/d)n. Determine from this ρ(x) and v(x), and then, using the current stationarity condition, find the exponent n. Get exact expressions for the current density and the current through the diode at a given voltage V. Electrode area S.