### Long Question Solution # Electrostatics - Long Question Answer 2

Question: Use the Gauss theorem to find the electric field intensity due to infinite plane sheet of charge.
Ans: Let us consider an infinite plane sheet with a uniform surface density σ. We have to find out the electric field intensity at a point P near the sheet. For this, consider a small area A whose walls are perpendicular to the sheet, extending by an equal distance on both sides of the sheet. By symmetry, the electric field intensity has the same magnitude on both sides of the surface and is directed normally away from the charged sheet. The flux crossing the side walls of the cylinder is zero because E is parallel to the side walls. Total electric flux passing through the two end flat faces,
Φ = 2 * EA
Net charge enclosed by Gaussian surface,
Q = σ * A
By Gauss theorem, we have
Φ = q/ϵ0
or, 2 * EA = (1/ϵ0) * σ * A
or, E = σ/2ϵ0
Thus, for points near the sheet, the electric field intensity is independent of the distance from the sheet.

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