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In an otherwise empty universe, a bar magnet spins pole-over-pole, emiting a magnetic wave (and also an electric wave (electromagnetism)?).

Since emitting an electromagnetic wave requires energy, it needs to come from somewhere. Will the energy needed come from the magnets's movement or its magnetism?

Or am I completely misunderstanding something?

EDIT: I somehow didn't notice this question when writing this one.

Debanjan Biswas
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jkoop
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3 Answers3

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According to the laws of electromagnetism, the spinning (or accelerating towards the fulcrum) magnet will loss its kinetic energy not its magnetism. So, it will slow down. Because the magnetism comes indirectly from the symmetrically arranged charged particles in a magnet, it will radiate its kinetic energy (assuming the symmetry of the particles is unchanged).

Hope this helps.

Debanjan Biswas
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    Could you say which laws of electromagnetism specifically guarantee that the magnet will slow its rotation instead of gaining thermal energy (and thus losing its magnetism) – Luke Pritchett Sep 04 '22 at 17:48
  • not just losing its kinetic energy but its angular momentum, as well; the latter will be transferred to the vector potential field thus the original angular momentum is always conserved. – hyportnex Sep 04 '22 at 18:11
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    you can probably calculate the rate of slowdown of a rotating magnet, to do this, you simulate rotating magnetic dipole with two oscillating dipoles, one on x-axis and other on y-axis and a phase difference of 90 degrees between them, using this you can calculate the electric and magnetic field due to both dipoles which will be equivalent to em field of rotating magnet, from here you can find out poyenting vector and hence you can calculate angular momentum of em field emitted, now use angular momentum conservation to calculate the rate of slow down of the dipole – Sourabh Sep 04 '22 at 18:54
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    @LukePritchett Yes, it will lose magnetism due to gaining some thermal energy. But the rate of losing magnetism for thermal energy can be neglected within a range of angular momentum. So, due to the rotation it will mainly loss its kinetic energy. – Debanjan Biswas Sep 04 '22 at 19:05
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Electromagnetic waves emitted by the magnet carry away momentum and energy, as per Planck's relations $$E=\hbar\omega, \mathbf{p}=\hbar\mathbf{k},$$ which means that there is a radiative back-action force on the magnetic moments emitting the radiation. Under the action of this force the magnetic moment might either

  • flip (or otherwise change its direction - depending on the type of magnetism and whether we discuss these moments classically or in quantum language)
  • transfer force/moment to the crystal (i.e., the bulk of the magnet)

The first effect would mean the randomization of the direction of magnetic moments, i.e., gradual loss of magnetization. The second effect would mean slowing the rotation of the magnet as a whole. Which of the two dominates depends obviously on how well the moments are anchored in their positions. For typical ferromagnets slowing is more likely, but there are probably "borderline" materials where interesting effects could be observed. Note also that the magnitude of the effect depends on many factors: how fast the magnet rotates, the geometry of the system, the size of the magnet (since flipping a few moments among billions would produce very insignificant changes), etc.

Roger V.
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Permanent magnets do not require an energy input and do not emit radiation - rather, the magnetic effect is produced by the atoms making up the magnet all facing the same direction. The only time an electric or other type of field would be produced would be if a conductive object was moving inside of the magnetic field around the magnet, which would induce an electric current in the moving conductor. Going on this, your magnet would spin forever, as your theoretical universe is devoid of any and all matter meaning there is no gravity, friction or other objects for it to interact with in any fashion and no way for it to lose momentum.

SuperGuy
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    Ok, so if there was a ferris object in the universe too, it would slow down? – jkoop Sep 04 '22 at 18:37
  • Depends. It the object is nonconductive and nonmetallic and there is no chance of it ever coming into contact with the spinning magnet, it would not have an effect on the spin. Now that I think about it, even if the magnet collided with something, it would still keep spinning, albeit with a slight loss of momentum and change of direction, as even with the second object, there's still nothing to exert friction or resistance. Even in the extreme example of the magnet colliding and sticking to a ferromagnetic object, the combination of the two would still spin together as one, never stopping. – SuperGuy Sep 04 '22 at 19:08
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    @SuperGuy That is not true. The magnetic field is present even without the presence of a "receiver". A rotating magnetic field (independent of its origin) will emit electromagnetic radiation. The magnet will eventually stop rotating if all of its rotation energy has been radiated away. – Jakob Stark Sep 05 '22 at 06:52