Final answer:
In physics, topological restrictions related to Gaussian surfaces used for planar symmetry include that the length of the Gaussian surface should be sufficiently large, the cross-section can be of any shape, and the end faces should be perpendicular to electric field lines for simplicity in calculations.
Step-by-step explanation:
Topological restrictions refer to certain conditions or limitations that must be considered when analyzing or designing systems, structures, or fields in various domains. In the context of physics, particularly when discussing planar symmetry and Gaussian surfaces, a Gaussian surface is a hypothetical surface used to apply Gauss's Law, which can help calculate the electric field of a given charge distribution. For a Gaussian surface to correctly apply to planar symmetry, its length does not have specific importance; rather, it should extend sufficiently far in both directions from the planar charge distribution. Its cross-section doesn't need to be square; it can be rectangular or of any other shape, as long as the symmetry is maintained. Lastly, the end faces do not necessarily have to be on opposite sides of the sheet, but it's important that they are chosen such that they are perpendicular to the electric field lines to ensure that the calculation simplifies properly.