Gauss Law for Magnetism,Non Instantaneous Field Propagation

Question

Is the magnetic force instantaneous? And, are all field lines established simultaneously? Otherwise, for example, the field line marked 'L' will take longer time to propagate than the ones above it, so there will be a net outward flux in the time when L is out and not yet in into the surface.What happens to Gauss Law then?

Are all the field lines established simultaneously, like 'L',that stretches out so far, and the straight one? If not, then the force between the magnets must increase with time.

Answer 1

The magnetic force propagates at the speed of light. If a magnetic dipole were suddenly created the magnetic field lines would be established simultaneously but not in their equilibrium positions. Instead the field lines would bend and oscillate in a similar manar as in an oscillating magnetic dipole. Since magnetic field lines are always loops, even when they are bent they will return so the magnetic flux through any closed surface will be zero as is required by Gauss's law for magnetism. Or in other words, even if the magnetic field lines are bent or slowed, they never start anywhere. There is no divergence of magnetic field lines since there are no magnetic monopoles. Gauss's law is alive and well.