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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.Gauss' Law for Magnetism
See, Gauss's Law in magnetism directly points to the fact that the net magnetic flux through any closed surface is zero. It does not say that the net flux through any closed loop is zero. Also by the statement that
div. B = 0 it is meant that the total flux through a unit volume enclosed by the closed surface is zero. But a loop is not a closed surface.It does not enclose any volume. Hence the net magnetic flux through a closed loop having a definite area and placed in a magnetic field is not always zero . It rather equals the scalar product of the magnetic field vector and the area vector. It is zero only when the loop is placed parallel to the direction of the magnetic field.
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No the net magnetic flux through an closed loop in not zero in presence of a magnetic field. Magnetic flux is equal to product of the magnetic field density and area enclosed by the loop. Hence it is not zero.