Electron gun; potentials around charged plates

Question

I know that an electron gun releases electrons by thermionic emission and accelerate the electron through charged plates, and that the electrons are not gaining any energy after they leave the gap between the plates. I'm confused about charges/potentials around the charged plates.

If you have two charged plates, one negative and one positive using an EHT, and earth the cathode. If you place an electron just next to the anode, not between the plates, what would happen to the electron? Well I'm told that it wouldn't move, but why?

I was also told that the field lines cancel outside the plates (given the plates are infinitely long and one of the plates are earthed) but why? If we say the surroundings are neutral, and earth the cathode, surely the field lines from the anode won't be cancelled, because the cathode is neutral?

CuriousOne · Answer

An infinitely long and wide plate will, indeed, produce a constant potential. The electrostatic force acting on a charge in a constant potential is zero, so in the ideal case the charges won't move. The solution to your paradox is that plates of infinite extensions don't exist.

What we mean by "infinite size plates" are plates that are so large that the potential sufficiently close to them is sufficiently constant. It can never be exactly constant, except on a conducting surface.

In the region between two parallel plates of different charge that are close enough together the potential is a linear function and the force is constant. This is a plate capacitor that can also be used to accelerate charges. Outside of the plates there is a substantial fringe field with a complicated field that extends all the way to infinity.

Electron gun; potentials around charged plates

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