Consider two large, parallel conducting plates, one with a charge density + and the other with charge density -.
The two opposite charges are attracted to the inside of the plates, as shown. We construct a cylindrical Gaussian surface, with one base area within a conducting plate and another base between the plates. If the area of each base is A, then we have
where E is the electric field at the base located between the parallel plates, since E = 0 on the base
inside the conductor plate.
Then, we have
Now, move on to a discussion of using Gauss's Law for the electric field of a line charge.