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In this video, they explain that magnetic force is an effect of electric force due to special relativity. https://www.youtube.com/watch?v=1TKSfAkWWN0

But then, the same authors explain in this video that magnetic is a particule property called intrinsic magnetic moment. https://www.youtube.com/watch?v=hFAOXdXZ5TM

I don't understand how can magnetism be both a relativistic effect of the electric force and an intrinsic property of a particule.

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  • $\begingroup$ Not knowing about the electrons magnetic dipole moment (an intrinsic, independent from surrounding circumstances, property) the induction of magnetic fields seems to be a relativistic effect only. After the observation of the intrinsic spin and the parallel to this magnetic dipole moment, for permanent magnets it was stated that the common magnetic field was induced by the alignment of the involved electrons. For a current carrying wire such a statement never was done. $\endgroup$ – HolgerFiedler Feb 16 at 15:50
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    $\begingroup$ Or is the electric force an effect of the magnetic force due to special relativity? $\endgroup$ – Aaron Stevens Feb 16 at 15:57
  • $\begingroup$ I wouldn't say it's an intrinsic property of a particle. If can be due to a fine substructure like charged quarks in a neutron or due relativistic quantum effects for the electron (QED). $\endgroup$ – Jan Bos Feb 16 at 17:48
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The symmetry of spacetime in special relativity requires that if the laws of physics include the possibility of electric fields, then they must also include the possibility of magnetic fields, and conversely. They cannot include one without also including the other.

A consequence of this is that in any situation that involves only an electric field in one coordinate system, there will be some other boosted coordinate system — that is, some other way of describing the same physical situation — that also involves a magnetic field. Conversely, in any situation that involves only a magnetic field in one coordinate system, there will be some other coordinate system — that is, some other way of describing the same physical situation — that also involves an electric field.

This is also true, by the way, for the magnetic field associated with a particle's intrinsic magnetic moment: there is necessarily some coordinate system in which it also involves an electric field.

So the correct statement is not that one or the other (electric or magnetic) is a purely relativistic effect; instead, the correct statement is that relativity implies that we can't have either one without the other. Even in situations where only one of them is present in some coordinate system, they will both necessarily be present in some other coordinate system that mixes the time and space coordinates of the original one.

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A particle with spin, such as an electron, has two different magnetic fields, one due to its motion through space and one due to its spin. (Note: The spin of an elementary particle can not be understood as that particle simply rotating in space, like the Earth spins on its axis. It is not a kind of “motion through space”.)

The magnetic field due to its motion through space can be considered a “relativistic effect” when the electron is moving uniformly. In the electron’s rest frame, this field completely disappears, and in other frames the magnetic field can be found by making a Lorentz transformation of the purely electrostatic field in the rest frame. So the magnetic field of a uniformly moving charge can be seen as a relativistic artifact of being in the “wrong frame”.

However, an accelerating electron has a magnetic field which cannot be made to disappear by choosing a particular reference frame. It is not the Lorentz transformation of some purely electric field. The magnetic field of an accelerating charge is not a relativistic artifact of being in the “wrong frame”, so you should not consider it a “just a relativistic effect”, even though electromagnetic radiation cannot be properly understood without relativity.

The magnetic field due to its spin is an intrinsic quantum-mechanical effect that cannot be made to disappear by choice of a reference frame. The magnetic field due to spin is not a relativistic artifact of being in the “wrong frame”, so, again, you should not consider it as “just a relativistic effect”, even though the proper understanding of spin does involve relativitistic quantum mechanics.

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Generating a static or quasistatic magnetic field does not require charges to move at relativistic speeds, so my answer to the title question is "no".

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    $\begingroup$ The OP didn't say that magnetism requires charges to move at relativistic speeds $\endgroup$ – Aaron Stevens Feb 16 at 16:59
  • $\begingroup$ @Aaron I agree. And your point is? $\endgroup$ – my2cts Feb 16 at 18:55
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    $\begingroup$ I don't think this answer is relevant to the question. There is a reason the questions here have bodies and not just titles $\endgroup$ – Aaron Stevens Feb 16 at 19:03
  • $\begingroup$ Nice narrative but if you don't mind I stick to the one question per post logic, that is, the first question in the post, the one in the title. $\endgroup$ – my2cts Feb 16 at 20:50
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    $\begingroup$ I agree, one question per post. But that doesn't mean you shouldn't look at the body of the post that actually clarifies the single question. In any case, that's why my vote counts just one time. If other people think your answer is useful, then more power to you. $\endgroup$ – Aaron Stevens Feb 16 at 22:08

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