If a parallel plate capacitor is formed by placing two infinite grounded conducting sheets, one at potential $V_1$ and another at $V_2$, a distance $d$ away from each other, then the charge on either plate will lie entirely on its inner surface. I'm having a little trouble showing why this is true.
In the space between the two plates the field $E = ( V_1 - V_2 ) / d$ satisfies Laplace's equation and the boundary conditions, from which I can derive the surface charge density is $\pm E / 4 \pi$. But how about the space above and below the capacitor? Certainly I can't just use superposition of the inner surface charge distributions to say that the field outside the capacitor is zero, (and thus the surface area charge density is zero), for this assumes there is no charge on the outer surfaces to begin with.
Any help clearing up this mental block would be greatly appreciated, thanks.