charge density of an infinite plane sheet (Fig. . ). We take the x -axis normal to the given plane.
By symmetry, the electric field will not depend on y and z coordinates and its direction at every point must be parallel to the x -direction. We can take the Gaussian surface to be a rectangular parallelepiped of cross sectional area A , as shown. (A cylindrical surface will also do.) As seen from the figure, only the two faces and will contribute to the flux; electric field lines are parallel to the other faces and they, therefore, do not contribute to the total flux. The unit vector normal to surface is in – x direction while the unit vector normal to surface is in the + x direction.
Therefore, flux E . Δ S through both the surfaces are equal and add up. Therefore the net flux through the Gaussian surface is EA . The charge enclosed by the closed surface is σ A .
Therefore by Gauss’s law, FIGURE . Gaussian surface for a uniformly charged infinite plane sheet.