Can magnetic fields be produced in other ways besides from a moving charge?

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!

• 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. Commented Mar 14, 2023 at 23:34
• @Aiden And how can you develop a time-varying electric field without charges in motion? Commented Mar 15, 2023 at 13:03
• @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. Commented Mar 15, 2023 at 16:25
• I'm not a physicist, but a magnet will produce a permanent magnetic field: en.wikipedia.org/wiki/Magnet Commented Mar 15, 2023 at 16:51
• 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. Commented Mar 15, 2023 at 19:34

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).

• Not just the electron, all charged elementary particles in the Standard Model have a permanent magnetic moment. Commented Mar 15, 2023 at 13:07

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.

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.