Two large parallel plates are located in vacuum. One of them serves as a cathode, a source of electrons whose initial velocity is negligible.
An electron flow directed toward the opposite plate produces a space charge causing the potential in the gap between the plates to vary as φp = ax4/3, where a is a positive constant, and x is (he distance from the cathode. Find:
(a) The volume density of the space charge as a function of x;
(b) The current density.