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We've all seen these magnetic field lines in physics classes. But how do these lines actually evolve in space around a magnet? Say you have a piece of iron that is demagnetised. And then suddenly it becomes magnetised. I doubt the magnetic field lines appear "instantly" around it. So, what is the speed of these lines "appearing"? Let’s not confuse this with the speed of "ripples" of this field, which is wave (not field itself) and propagates at $c$.

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Say you have a piece of iron that is demagnetised. And then suddenly it become magnetised.

This is a difficult experiment to perform. However, we can instead make a solenoid and suddenly turn on a current through the solenoid. A solenoid has roughly the same external magnetic field as a bar magnet, so it is a good and very close substitute for your proposed experiment.

I doubt magnetic lines appear "instantly" around it. So, what is the speed of these "appearing"? Lets not confuse this with the speed of "ripples" of this field, which is wave (not field itself) and propagates with c.

There is no confusion, the speed of the appearing of the field lines is indeed $c$. This type of configuration is well known and well studied. It is called a “loop antenna”. As with all antennas, the signal propagates at $c$. If you turn on a current at time $t$ then at time $t+d/c$ the magnetic field lines will appear at a distance $d$ away from the loop antenna.

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  • $\begingroup$ How long would it take for a random orientation of spins to align themselves spontaneously? In other words, what is the minimum amount of time to cross the Curie point below which there appears a "permanent" magnet? $\endgroup$
    – hyportnex
    Jan 6, 2020 at 22:45
  • $\begingroup$ Sorry, that is beyond my knowledge $\endgroup$
    – Dale
    Jan 6, 2020 at 23:09
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Actually, any disturbance in an electromagnetic field propagates at the speed of light. If a magnet suddenly appeared at a point in space, its field would propagate outward at $c$. At a distance D away from the magnet, no change in the field would be detected until a time $t=D/c$ after the magnet appeared.

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    $\begingroup$ Was it proved somehow? $\endgroup$
    – m8labs
    Jan 6, 2020 at 21:15
  • $\begingroup$ Maxwell's equations are extremely reliable, and they show unambiguously that EM disturbances propagate at the speed of light. An experiment to prove it (not counting propagation of waves from a periodically varying source) would be difficult but not impossible; however I haven't heard of any such experiment. $\endgroup$
    – S. McGrew
    Jan 6, 2020 at 21:37

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