State gauss theorem. Apply this theorem …

Gauss"s Theorem: It states that net electric flux diverging normally from a closed surface is equal to 1/ε₀ times the net charge enclosed by the surface.

Let electric charge be uniformly distributed over the surface of a thin, non-conducting infinite sheet. Let the surface charge density(i.e., charge per unit surface area) be . We have to calculate the electric field strength at any point distant r from the sheet of charge. To calculate the electric field strength near the sheet, we now consider a cylindrical Gaussian surface bounded by two plane faces A and B lying on the opposite sides and parallel to the charged sheet and the cylindrical surface perpendicular to the sheet (fig) By symmetry the electric field strength at every point on the flat surface is the same and its direction is normal outwards at the points on the two plans surface and parallel to the curved surface.

Total electric flux