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So they ended up using a closed cylinder with ened caps of area A, arranged to pierece the sheet perpendicularly. I know that the E field is going to hit the two end caps. So your going to have 2 EA's. But if you find the flux through the opposite end wouldn't it be E cos(180) A = -EA. then the other side would be E cos(0)A = EA, so wouldn't the EA's cancel out? The book shows them both being positive:

Eo(EA + EA) = [tex]\delta[/tex]A.

E = [tex]\delta[/tex]/(2Eo).

Thanks.