What is the electric field due to a large, thin charged sheet made of some nonconducting material?
We construct a cylindrical Gaussian surface, and place it symmetrically in the charged sheet as shown in the above figure. Let the area of each top surface of the cylinder be A, and the surface charge density on the sheet be .
Applying Gauss's Law to this cylindrical Gaussian surface gives
and we note qenc = A.
Therefore,
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