The case for infinite sheets are simple enough, and also for a disk of finite size, which can be derived as in the picture.
title edited to specify sheet is finite.
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Adenine
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1Check out this link Adenine. It has a really nice explanation. – Prasad Mani Oct 22 '16 at 15:06
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@PrasadMani it seems that link also explains equations involving sheets of infinite area. in the case of finite ones, shouldn't the electric vary with the distance? – Adenine Oct 22 '16 at 15:15
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What do you mean by "near a 2D square sheet"? – Spirine Oct 22 '16 at 15:18
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Of course it will. Infinite sheet is just an approximation. Was your question about finite conducting sheet? – Prasad Mani Oct 22 '16 at 15:19
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@Spirine near in the sense at point P which is at a distance d away from the sheet. I want to know E at P. – Adenine Oct 22 '16 at 15:21
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@PrasadMani Yes, sorry the original title wasn't clear enough. – Adenine Oct 22 '16 at 15:22
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Okay, then look at this – Prasad Mani Oct 22 '16 at 15:24
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@PrasadMani this problem seems similar enough, if we assume that point P at which I want to know the electric field is vertically above the midpoint of the horizontal sheet, I would argue that we have enough symmetry to the problem to use Gauss' law? – Adenine Oct 22 '16 at 15:29
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Not entirely satisfactory probably and i am posting links because i dont know the answer myself and am searching for it but this is where you should go next if you havent already seen it – Prasad Mani Oct 22 '16 at 15:53