The electric field between two parallel plates is independent of their separation when the distance is negligibly small, as derived using Gauss's Law. By applying Gauss's Law to a sheet of charge, the electric field can be shown to be perpendicular to the surface and uniform across the plates. The total electric field between the plates is the sum of the fields from each plate, which remains constant regardless of separation. This concept also applies to infinitely large planes, where no distance scale affects the result. The discussion emphasizes the importance of using a Gaussian pillbox for accurate derivation.
