Using the divergence theorem, evaluate the total flux of a magnetic field B(r) across the
surface S enclosing a finite, connected volume of space V, and discuss its possible
dependence on the presence of an electric field E(r).
The Attempt at a Solution
The first part was pretty straightforward. Using the Maxwell equation in conjunction with the divergence theorem, it is easy to see that the magnetic flux across a closed surface is 0. The next part somewhat confuses me. My initial thought is that the divergence of B being 0 holds for all cases and therefore the presence of an electric field should have no bearing on the magnetic flux. However, I am not 100% sure though. Any help will be appreciated.