Regarding your first issue, I am under the impression that I am supposed to integrate over the area of the surface which the field is passing through. In this case, the field is passing through the circular portion of a Gaussian cylinder, as the side lengths of the cylinder do not contribute to...
Problem #1
A slab of thickness 2a (extending infinitely in the y and z directions) with non-uniform charge density is parallel to the yz-plane. The charge density is given by
ρ(x) = γx2, -a < x < a where γ is a constant.
0, a < |x|.
(a) Use Gauss's law plus symmetry to find...