Fiels linesMagnetic Flux**Field lines**

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.

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    $\begingroup$ Changes in magnetic field (and hence magnetic field itself) travel with speed of light. Bar magnet picture could be confusing. Think of a wire. When you switch on current through it then it is clear that magnetic field will expand out in circles (rather than directed lines), and so Gauss's law would be fine. $\endgroup$
    – user10001
    Commented Jul 26, 2012 at 17:19
  • $\begingroup$ The question is not clear. What's the imagined violation? The field lines are produced in many closed loops that grow and leave behind the static field at long times, so that Gauss's law is never violated. $\endgroup$
    – Ron Maimon
    Commented Jul 27, 2012 at 6:40
  • $\begingroup$ @Ron Maimon : I've actually imagined field lines as "snakes", each with a head and a tail. $\endgroup$ Commented Aug 7, 2012 at 16:38
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    $\begingroup$ @SwapnanilSaha: well, stop doing that. Imagine them as rings. Only E fields are snakes. $\endgroup$
    – Ron Maimon
    Commented Aug 8, 2012 at 16:40
  • $\begingroup$ @Ron Maimon : Also the G ones, right? $\endgroup$ Commented Aug 9, 2012 at 12:58

1 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.


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