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Assume there is an infinitely large plane with a charge density $\sigma$. I understand how to derive, using Gauss' Law, that $E = \frac{\sigma}{2\epsilon_0}$ is the electric field at a distance $r$ from the plane.

However, intuitively, I don't understand how this could be true. Shouldn't the electric field be more powerful closer to the plane, since the electric field falls of as $\frac{1}{r^2}$? The larger I make $r$, the further it is from every point, meaning the electric field should decrease - shouldn't it?

Any help understanding this would be appreciated.

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    $\begingroup$ Think about what "infinitely large plane" means in this case. $\endgroup$
    – Kyle Kanos
    Commented Oct 9, 2014 at 13:32
  • $\begingroup$ But, by making the distance from the plane longer, is the point not becoming further from every point on the plane at the same time? $\endgroup$
    – Cisplatin
    Commented Oct 9, 2014 at 13:33
  • $\begingroup$ This is true, but those "far away" charges of the sheet cancel out because the sheet is infinite. $\endgroup$
    – Kyle Kanos
    Commented Oct 9, 2014 at 13:38
  • $\begingroup$ There is nothing in reality that implements an "infinitely large plane". This is an abstraction that asks you to assume a finite plane and estimate the scaling of the total charge and the fields that are generated by the charge with size. The result may be a bit counterintuitive, though. $\endgroup$
    – CuriousOne
    Commented Oct 9, 2014 at 14:24
  • $\begingroup$ Infinity is a wonderful thing. It's even more wonderful in mathematics, where it turns out there's an infinite number of different infinities. $\endgroup$
    – Carl Witthoft
    Commented Oct 9, 2014 at 14:28

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Here's a simple way of looking at it:

If you are close to an infinite plane, you may be feeling stronger attraction by every individual part of it, but "more" of those parts are pulling you at a significant angle. This way, a lot of the attraction is canceling out. As it happens (this is anything but coincidence though), these two opposite effects exactly cancel eachother out when you move away from (or closer to) the plane.

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