I'd like to know whether my sense of Gauss's Law is correct here.
Suppose I have a cube of side length $L$ filled uniformly with electric charge. Let's say I use as my integration surface a cube enveloping the cube of charge that has side length $2L$.
In this situation, Gauss's Law holds with my choice of integration surface, and I believe the choice is sensible as well. As long as my surface encloses the charge density I'm trying to find the electric field of and only that, the dimensions of the surface doesn't matter. Does this sound reasonable?
Could one use Gauss's Law in this scenario to solve for the electric field at points outside the charged cube? My intuition is no, as Gauss's Law is only useful when considering the electric fields for regions enveloping a charge density. I'd need to draw a Gaussian surface around the point, and I would reason that since there is no charge within that region then there is no electric field. However, this could be very wrong or right for the wrong reasons, and I'd like to clarify this in my brain.