I'm given a problem involving two parallel conducting plates a small distance apart. One has charge Q, the other is neutral. I'm asked to find the surface charges on all faces.
I began by creating a Gaussian cylinder with each face terminating within one of the two plates. Since the electric field inside a conductor is zero, the net charge must be zero and whatever charge on the interior surface of the charged plate, the uncharged plate must have the same one, but opposite in sign.
Furthermore, the surface charges on the charged plate must sum to Q and on the uncharged plate to 0 by conservation of charge. Here's where I'm stuck -- aren't there many possible charge configurations that satisfy these conditions?