Gauss's Law=The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.
Electric field due to a uniformly charged infinite plane sheet : Suppose a thin non-conducting infinite sheet of uniform surface, charge density .
Electric field intensity on either side of the sheet must be perpendicular to the plane of sheet having same magnitude at all points equidistant from sheet.
Let P be any point at a distance r from the sheet.
Let the small area element
are perpendicular, on the surface of imagined cylinder, so electric flux is zero.
are parallel on the two cylindrical edges P and Q, which contributes electric flux.
Electric flux over the edges P and Q of the cylinder is
The charge density [where S-area of circle]
vecotrically
where is a unit vector normal to the plane and going away from it.
When , E is directed away from both sides. Hence electric field intensity is independent of r.
When , E is directed away from both sides. Hence electric field intensity is independent of r.
Note : For conducting sheet, the surface charge density on both the surface of sheet will be same