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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?

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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.

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  • $\begingroup$ So If there is an electron just next to a plate capacitor, would it be affected by the electric fields? $\endgroup$
    – RelativisticDolphin
    Jan 9, 2016 at 20:10
  • $\begingroup$ Yes, it would be. The motion may be very slow because the potential may change very slowly, but there would be a motion. Like I said, the ideal case does not exist, it's just a convenient approximation. $\endgroup$
    – CuriousOne
    Jan 9, 2016 at 20:11
  • $\begingroup$ That's the bit I'm struggling to understand. If the 'earth' is neutral in terms of charge, and if we earth the cathode, it's just like having a positive plate on its own. So why would the field lines from the anode to the surroundings be cancelled? $\endgroup$
    – RelativisticDolphin
    Jan 9, 2016 at 20:23
  • $\begingroup$ If you look at the equipotential surfaces very near to a plate, they show an almost constant potential close to the surface. The larger the plate, the more constant the potential will be near the surface. The more constant the potential, the less force will be acting on charges. "Earth" is the hypothetical potential at infinity and we always set it to 0. A positively charged plate has a finite potential but as long as we are close enough (compared to the nearest other potential) it doesn't matter. Maybe I don't understand your setup correctly? $\endgroup$
    – CuriousOne
    Jan 9, 2016 at 20:39
  • $\begingroup$ I think I might be making a huge mistake but I'm not sure where.... I'll just carry on asking and we'll figure out $\endgroup$
    – RelativisticDolphin
    Jan 9, 2016 at 20:42

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