Final answer:
Magnetic flux through any closed surface is zero, reflecting the continuous nature of magnetic field lines. The areas of the surface do affect partial magnetic fluxes, but the net magnetic flux remains zero. For electric flux, the net flux through a closed surface is zero if there is no net charge within, but areas and orientation affect partial fluxes.
Step-by-step explanation:
When discussing the concept of magnetic flux through a closed surface, such as a box, it is crucial to remember that according to Gauss's law for magnetism, the net flux is always zero. This is because magnetic field lines are continuous; they do not begin or end but form closed loops. Similarly, for electric flux, the net flux through a closed surface is also zero if there is no net charge enclosed by the surface. If there are charges inside the volume enclosed by the surface, then the electric flux is proportional to that net enclosed charge.
Therefore, the areas of the surfaces of the box do affect the partial magnetic fluxes, but when considering the entire closed surface, the sum of these partial fluxes will always be zero for a magnetic field. This is different for an electric field where the surface area and the orientation of the field with respect to the surface determines the amount of flux through that particular surface area.