Electric displacement in plate capacitor

[musemonkey]

Suppose there's dielectric material in inside a parallel plate capacitor with plate charge densities ±σ. What's the electric displacement D?

I've seen solutions that draw a Gaussian surface around one of the surfaces and argue that the enclosed charge is Aσ and the flux of D is Aσ therefore D=σ.

But what about the contribution of the other plate? If one takes it into account, it makes an equal contribution yielding a total D=2σ. How is this reasoning flawed? I know it to be wrong because one can derive the field from the displacement and the bound charges and then get the field again by considering the bound and free charges. The two field calculations are inconsistent if D=2σ.

Thanks.

 

[musemonkey]

I figured it out

but can't delete my post.