Chapter-1|Electric Charges and Fields | NCERT 12th Physics:
Applications of Gauss' Theorem:
(II)Field Due to Thin Infinite Plane Sheet of Charge:
We consider a thin, infinite plane sheet of charge with uniform surface charge density Sigma(σ).We want to calculate its electric field at point P, at distance r from it.
Now, to form a Gaussian surface on the sheet we choose cylindrical Gaussian surface of cross sectional area A and length 2r with its perpendicular to the sheet.
On the curved surface of the cylinder, E and n^ are perpendicular to each other. Therefore flux through curved surface area=0. Flux through the flat surface = EA+EA=2EA. Total electric flux over the entire surface of the cylinder-
From above E is independent of r, The distance of the point from the plane charge sheet.