Capacitors: How to determine the charge density at each surface?

[AlonsoMcLaren]

Suppose we have two metal plates, one with a charge density of 3 C/m^2, the other -3C/m^2

We are told that the charge density on surfaces 1 and 4 are zero and the charge density on surface 2 is 3C/m^2, on surface 3 is -3C/m^2

Any reason for that? Is it possible that the charge density on surface 1 is 1 C/m^2, on surface 2 is 2 C/m^2, on surface 3 is -2 C/m^2, on surface 4 is -1 C/m^2? I don't see it violating Gauss law..

 

[cragar]

The E field inside the conductor needs to be zero, do you see any problems.

 

[AlonsoMcLaren]

The E field inside the conductor needs to be zero, do you see any problems.

So what is the charge density on the surfaces 1, 2, 3, 4 if the upper plate has a total charge density of 3C/m^2 and the lower plate has charge density of 0?