The net
magnetic flux out of any closed surface is zero. This amounts to a
statement about the sources of magnetic field. For a magnetic dipole, any
closed surface the magnetic flux directed inward toward the south pole
will equal the flux outward from the north pole. The net flux will always
be zero for dipole sources. If there were a magnetic monopole source, this
would give a non-zero area integral. The divergence of a vector field is
proportional to the point source density, so the form of Gauss' law for
magnetic fields is then a statement that there are no magnetic monopoles.
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