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From my understanding, a moving charge produces a magnetic field, and a non-moving charge does not produce a magnetic field. However, I'm wondering if there's a way for a magnetic field to be produced without involving any charged particle at all. I was thinking about a bar magnet, or some other permanent magnet made of ferromagnetic material, but if the electrons within the material interact with each other, then would that count as a charge? Thanks for any help!

Daniel Li
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    A magnetic field can also be generated with a time-varying electric field. For example, light is an electromagnetic wave which can propagate though space without any charge around. – Aiden Mar 14 '23 at 23:34
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    @Aiden And how can you develop a time-varying electric field without charges in motion? – Sam Gallagher Mar 15 '23 at 13:03
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    @SamGallagher A time-varying magnetic field could generate a time-varying electric field. I realize this is somewhat circular. Of course when the EM wave is first generated, it requires the motion of some charge or moment. But once created, it can propagate arbitrarily far from any source and after the source is gone. – Aiden Mar 15 '23 at 16:25
  • I'm not a physicist, but a magnet will produce a permanent magnetic field: https://en.wikipedia.org/wiki/Magnet – Flydog57 Mar 15 '23 at 16:51
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    The magnetic field of a material (such as a magnet) will come from the motion of the electrons and/or the spin of the electrons (see Juan Perez' answer). This includes charge in the generation of the magnetic field in the electron motion case, but not in the electron spin case. – 2ndQuantized Mar 15 '23 at 19:34
  • @Aiden It's a matter of perspective, but even saying that a time-varying field "generates" another implies there is causality (at least to the student, absent careful clarification), while instead the fields are coupled, not causal. The existence of one implies the existence of the other, but there is no time delay (or else at the source you could have a changing electric field without a changing magnetic field for a brief period of time). Charges are the ultimate source of the electromagnetic field, and in my opinion this is the key point – Sam Gallagher Mar 16 '23 at 12:46
  • @SamGallagher Your comment is the point of my answer below. I didn't have time to include https://en.wikipedia.org/wiki/Jefimenko%27s_equations which show that even the CMB we observe today was generated by $q, \vec j, \dot q, \dot{\vec j}$ on our very distance past light cone, and not by changing fields a distance $\lambda = hc/k_BT$, ($T=2.7,$K), in front of our dishes. – JEB Mar 16 '23 at 18:33

3 Answers3

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Electrons have an intrinsic magnetic moment, which generates a magnetic field. This magnetic moment is unrelated to any motion, and it is a consequence of the electron's spin (which isn't a movement).

Peter Mortensen
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Juan Perez
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    Not just the electron, all charged elementary particles in the Standard Model have a permanent magnetic moment. – Mauricio Mar 15 '23 at 13:07
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Perhaps magnetic monopoles exist... Many theories suggest that they should exist, but they might be enormously rare.

If they do exist then they would produce a magnetic field that had non-zero divergence. The magnetic fields generated by moving electrons obey Gauss's law: $\mathbf{\nabla}\cdot\mathbf{B}=0$ But the field generated by a monopole would have $\mathbf{\nabla}\cdot\mathbf{B}\propto \rho$ the density of magnetic charge.

Magnetic monopoles would be a form of magnetism that was entirely unrelated to the motion of particles with electric charge. They are theoretical but many physicists think that they probably do exist, but are too massive to make in particle colliders, and to rare for natural ones to ever be detected by luck.

James K
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The magnetic field at a point/time is generated by currents, and time-varying currents on the past light-cone. That's it. A dipole is just a current in a small loop.

The time varying current may also generate an electric field that looks like it's inducing the magnetic field, but it's not.

JEB
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