Which of these two configurations will actually occur? (Or perhaps
are both possible?)
We know the field due to a single infinite sheet of charge. So we can
superpose it for 4 sheets of charge. Doing this proves configuration
1 *cannot* occur because it leads to nonzero fields inside the metal
of the plates. Please check this for yourself.
Fine. But now the question is: Does configuration 1 violate Gauss'
law? Answer: No. No matter how you position the endcaps of your
Gaussian surfaces (in the metal or in the vacuum), Gauss' law is
satisfied. Again, please check this for yourself.
So if we only knew Gauss' law, we could not disprove configuration 1.
Nevertheless we know it cannot occur. So what is wrong with it then?
Answer: it is energetically too costly. The field energy in each
region is proportional to E^2. Configuration 1 would require
infinitely more energy than configuration 2.
If we think about each side as a separate plate, we have 4 plates in
all. This is a set of series capacitors and there is a unique
solution to where the charges go, imposed by requiring the energy to
be a minimum. Gauss' law alone will not tell you this. You guys
taught me about this earlier: