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When we try to find the electric field between the capacitor plates, what is the right way to do it? This is one of the ways I've seen and I don't understand why:

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Using a Gaussian cylinder on the positive metal plate, E inside is zero while E outside is $ \frac { \sigma}{ \epsilon_0}$

But from what I know about conductors is that the charge uniformly spreads itself out on the surface, not only on the bottom, so why do we take a cylinder that only takes into account the charge on the bottom and not on the top as well?

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  • $\begingroup$ So the electric field due to one metal plate without taking into account the other metal plate, should be $E=\frac{\sigma}{2\epsilon_0}$ , correct? $\endgroup$ – cazanova Jul 9 at 19:18
  • $\begingroup$ @cazanova yes it is correct for a isolated metal plate $\endgroup$ – Nitin Shaji Jul 9 at 19:47
  • $\begingroup$ Yes, that is correct. I have deleted my comment and have posted it as an answer as I think it pretty much answers your question. $\endgroup$ – Dvij Mankad Jul 9 at 20:29
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You are implicitly taking care of the fact that you have charges on the other plate as well. You are doing it when you assume that $E$ is zero outside (i.e., below the bottom plate). Otherwise, you would have $E=\frac{\sigma}{2ϵ_0}$ both above the bottom plate and below the bottom plate.

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