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In ferromagnetic context I've read many textbooks that mention "magnetic charges". From what I understood, there is no such thing as ’ magnetic charges’, however, although the notion is incorrect, it is a very useful idea for the description of demagnetizing fields, also seems to be widely used and accepted. As far as I know it is the existence of free-poles which gives rise to H_d, but this is again, based on the idea of a magnetic charge density on a surface. I've also read H_d can appear thanks to electric currents. How is this possible?

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  • $\begingroup$ There is nothing incorrect about the notion of magnetic charges, they are defined as the source of the macroscopic magnetizing force field: $\text{div}\mathbf H = \rho_m$. What is incorrect is to call these "free" poles, they are not "free" because they are tied to the macroscopic magnetized matter. $\endgroup$
    – hyportnex
    Feb 5, 2023 at 17:19
  • $\begingroup$ @hyportnex probably I didn't choose my words carefully but when I mention free poles I mean that the piece of the material has ends, like a rectangular prism with M along an axis, so you clearly have two poles that lead to a demagnetizing field. A toroid for example, would have no free poles . Now, this idea is not right because as I mentioned in my question it is based on the existence of "magnetic charges", as I said, it is useful but not truly accurate. Maybe this work helps to clarify. reprints.gravitywaves.com/Magnetism/… $\endgroup$
    – Myr89
    Feb 5, 2023 at 18:08
  • $\begingroup$ If you think that $\mathbf H$ is useful then so it is its divergence. In a toroid its divergence is zero but so is that of the induction field $\mathbf B$, does that make the latter useless? Don't forget $\text{div}\mathbf B=0$, everywhere. We are talking about macroscopic fields within ferromagnetic material where $B$, $H$, $M$ all being spatial and temporal averages of some underlying microscopic fields, and are equally physical or non-physical, neither is more so than the other. $\endgroup$
    – hyportnex
    Feb 5, 2023 at 18:37

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'Magnetic charges' are mathematical constructs, not physical quantities, that are useful intermediate quantities in calculating the H field.

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