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Two large parallel plates are located i...

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.

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