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We consider an infinitely large plane non-conducting sheet of charge having a inform surface charge density to on one plane surface. From the symmetry of charge distribution we can conclude that the electric field due to this charge is normal to the sheet and because the charge is positive the field points away from the sheet. We now choose a cylindrical Gaussian surface of cross sectional area A and a length 2r. The axis of the cylinder is normal to the sheet S and the sheet divides the Gaussian surface into two equal halves. 

 

Since the electric field is tangential to the curved surface of the cylinder, the electric flux through it is zero. The field being normal to and constant in magnitude at the flat surfaces of the cylinder the flux through the each of the flat surface is ES. This implies that the total flux through the cylindrical surface is 2ES (as there are two flat surfaces). The total electric flux  through this Gaussian surface is, therefore, 2ES. 

There area of the sheet of charge enclosed inside this cylindrical surface equals the cross-sectional area of the cylinder. Therefore, the charge q_i enclosed inside this Gaussian surface is ?S. Now, as per Gauss's law. 

Clearly, E is independent of r, the distance of point from the plane charged sheet. If  the sheet carries +ve charge, the electric field is uniform, and points normally away from the plane charged sheet on its both sides. If the sheet carries -ve charge, the electric field is uniform, and points normally into the plane sheet on both sides.