What is the electric field near a uniform plane of charge?

The plan is to use Gauss's Law by drawing a gaussian surface.

Symmetry dictates that the field be pointed upward.

If we draw a gaussian surface that is a cube, we can easily evaluate the flux. The electric field is parallel to sides of the box so the flux is zero for those surfaces (see side view below). The field is a constant across the top and bottom so they can be taken outside the flux integral.

The flux is then (2 E A) when we add the top and bottom parts. (A is the area of the top or bottom of the cube). The charge enclosed in the box is also proportial to A.

The electric field is then found to be: