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I saw this in a lecture about gausses law in application to infinite charged planes:

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How is it possible that the electric field above the top plane and below the bottom plane is always zero, given that the effect of each plane near its outside surface contributes to the electric field much more than the other plate according to Coulombs Law?

Also, how is it possible that the electric field stays constant between the two assuming they are infinite planes no matter the distance between them by the same principle?

(I assume this deals with the effectively infinite contribution in the +i and -i direction of each individual charged particle.)

Can someone give a more detailed explanation of this?

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  • $\begingroup$ You state "given that the effect of each plane near its outside surface contributes to the electric field much more than the other plate" but this is not a given. It may indeed surprise. $\endgroup$
    – my2cts
    Aug 6, 2019 at 23:29

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The electric field from a uniformly charged infinite plane is constant, it doesn't fall off with distance. Coulombs Law is a statement about the force between two charged particles, which is why it works out differently when you talk about planes. You can actually apply Coulombs Law to reach that conclusion:

$$ V(r) = \frac{1}{4\pi\epsilon_0} \int_{plane}\frac{\sigma dA}{r}$$

To understand it intuitively, imagine the plane in front of you. No matter the distance separating you both, the plane looks the same. So there is no reason for the electric field to change.

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