1. The problem statement, all variables and given/known data In a vacuum diode, electrons are "boiled" off a hot cathode, at potential zero, and accelerated across a gap to the anode , which is held at positive potential V0. The cloud of moving electrons within the gap(called space charge) quickly builds up to the point where it reduces the field at the surface of the cathode to zero. From then on a steady current I flows between the plate. Suppose the plates are large relative to the seperation(A>>d^2), so that edge effects can be neglected. Then V, rho, and v(the speed of the electrons) are all functions of x alone. a) Write Poisson's equation for the region between the plates. 2. Relevant equations [tex]\nabla^2[/tex] V= [tex]\nabla[/tex] [tex]\cdot[/tex] E ; If I did not format latex correctly , then here is what I alway trying to write out below: del^2 V= del E V=[tex]\int[/tex] E [tex]\cdot[/tex] dl 3. The attempt at a solution to get V , I easily integrate E dot dl. How would I obtain the electric field of a parallel plate capacitor. I don't need V to obtain the Poisson equation since: [tex]\nabla^2[/tex] V = [tex]\nabla[/tex] [tex]\cdot[/tex] E once I calculate E, how would I find the divergence of E? would I set my coordinate system to a cartesian coordinate?