Two large parallel plates are located in vacumm. One of them serves as a cathoide, a source of e

Two large parallel plates are located in vacumm. One of them serves as a cathoide, a source of electrodes whose initial velocity is neglible . An electrones flows direcee toward the opposite plate produces a space charge causing the potential int eh gap betwnen the plates to between the plates to very as `varphi = ax^(1//3)`, where `a` is positive constant, and `x` is the distnaace form the cathode. Find: (a) the volume density of the space charge as a funciton of `x`, (b) the current density.