Ok I took E&M about 3 years ago and decided I needed to review it. I'm up to gauss' law and am getting confused about one thing. If you have two infinitely long oppositely charged plates, solving for the total e field inside is done by making two gaussian surfaces that enclose each plate. Doing this gives the e field to be a constant between the plates. My question is, why can't I make a gaussian "pillbox" inside the plates and enclosing zero charge and conclude that the flux through that surface is zero since the field goes in one side and leaves through the other? Obviously I'm making a mistake here somewhere because the field in between the plates is NOT zero but I can't figure out what the mistake is.