Integral form of Gauss' Law, Parallel Plate Capacitor

[jajay504]

Homework Statement

If one were to consider a parallel plate capacitor with a distance d between them connected to a battery and a vacuum space between the plates. Will the integral form of Gauss' Law to any closed surface between the plates that does not cross either plate hold? If not, what in Gauss' Law would prevent this from working?

Homework Equations

Gauss' Law

The Attempt at a Solution

I know that Gauss' law works in cases where there is high degree of symmetry.
I also know that the integral form describes an integration of fields. However, after a function is integrated, a lot of information is lost. A non-zero charge density cannot, under any circumstances, give rise to a an electric field that vanishes everywhere.

 

[lightgrav]

There's a distinction between a Law being valid (ie, "holding" true), and being useful.
Gauss' Law would merely say that there's zero total charge inside the surface ... which we already knew ... there's only vacuum in there, after all.
But since you need to integrate over the whole surface Area, you can't find the flux inward thru the top separately from the flux that leaves out the bottom => so you can't find the surface charge density. It still "works" in the sense that it doesn't lie ("0=0"), but it doesn't "work" in the sense of being useful to solve for E, or σ, or Q ...