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https://en.wikipedia.org/wiki/Force_between_magnets

In this article, for the ampere model section, wiki talks about how we can think of permeant magnets as having current flowing through them and it is this current which causes magnetic field. Now, my question is how is there current flowing through a magnet? does this mean there is a potential difference?

Certainly I have not felt "shocked" when I ever touched a magnet, so it certainly seems like it is not the case. Or is this like something which we introduce into existence to simplify calculations? Further, disregarding if it is real or not, could we potentially use ampere's law on these type of loops?

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The current referred to in the Wiki article are meant to give you a visual in your mind about orbital and spin magnetic moments. There are no currents like you would think of in an electric circuit flowing through ferromagnetic materials.

Ferromagnetic materials become magnetic because their magnetic moments spontaneously align below what is called the Curie temperature. Magnetic moments are separated into two kinds: 1)orbital, which are related to the orbital angular momentum of the valence electrons around the nucleus, and 2)spin, which are related to the intrinsic spin angular momentum of the electron.

In metals like nickel, cobalt and iron, it is the electrons that sit in a narrow band (called the d band) that align and give these metals their ferromagnetism. Thinking of a spinning electron as a small current loop producing a magnetic dipole sometimes aids in visualizing the nature of the phenomenon. But as far as we know, electrons do not have a structure, so ultimately this is only an aid to us, not a real description. The spin of the electron and its associated magnetic moment is just something it has.

To the point of using Ampere's law, I have not seen that done in any calculation on ferromagnets that I've read.

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In a permanent magnet, you can think of each atomic dipole moment as being produced by a tiny loop of current. Then the magnetic effect from each segment of current loop within the magnet is canceled by an adjacent loop with current in the opposite direction. Only the current segments at the surface are not canceled. The magnetic field produced is the same as that which would be produced by a current flowing around the outer surface of the magnet (or by a current carrying solenoid of the same shape and dipole moment). (The dipole moment per unit volume associated with the current flow would have to match the magnetization of the material of the magnet.) One can use the Biot formula with the current in a similar solenoid to estimate the field strength inside or outside the magnet. (One might estimate the dipole moment of a magnet by suspending it from a thread and measuring the period of oscillation in the earth's field.) For a long narrow magnet or solenoid, you can put half an Ampere loop lengthwise inside and the other half outside where the field is very small.

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CGS wrote in his answer

Thinking of a spinning electron as a small current loop producing a magnetic dipole sometimes aids in visualizing the nature of the phenomenon. But as far as we know, electrons do not have a structure, so ultimately this is only an aid to us, not a real description. The spin of the electron and its associated magnetic moment is just something it has.

What if we treat the electron as an elementary particle with both an intrinsic electric field and an intrinsic magnetic field?

The electrons intrinsic magnetic field

Ampère deduced his law in 1820th. This time according to Wikipedia he defined a electrodynamic molecule (bolt highlighted by me):

Ampère also provided a physical understanding of the electromagnetic relationship, theorizing the existence of an "electrodynamic molecule" (the forerunner of the idea of the electron) that served as the component element of both electricity and magnetism. Using this physical explanation of electromagnetic motion, Ampère developed a physical account of electromagnetic phenomena...

That electrons have a magnetic field was found in 1920th, 100 years later. The value of the electrons magnetic moment is a constant and by this an intrinsic (independent from surrounding circumstances) property of the electron. Our usual view on the electron as only a charge is superficial and historically charged. In reality the electron is a charge and a magnet, with both fields of constant strength.

This view greatly simplifies the understanding of magnetic phenomena:

  • permanent magnets are such because of the self-alignment of the involved subatomic particles
  • the dismagneotisation of magnets by rising temperatures happens due to the more intensive thermal movement of the subatomic particles which destroy the self-alignment of the magnetic dipoles
  • the condensation of some gases by ultra-cold temperatures to self-aligned system (Bose Einstein condensate) happens again because of the suppressed thermic motion and the asymmetric magnetic moments in the molecules
  • and finally, the conclusion that costs the most to overcome, magnetic fields from coils occur again because of the alignment of the magnetic dipoles of the involved electrons.

The spin as a secondary phenomenon of the electrons magnetic field

What if we treat spin as a secondary phenomenon of the magnetic dipole of electrons?

Then the Lorentz force is explained as follows. An electron moves with its kinetic energy into an external magnetic field. The magnetic dipole of the electron is aligned to this field and during the alignment a photon is emitted (please note that the electron actually radiates). The photon has a recoil moment and the electron is deflected laterally and at the same time misaligned. This process is repeated as long as the kinetic energy of the electron is exhausted and the electron has come to a standstill in the middle of its spiral path.

Follow such treatment, the spin is a phenomenon of the intrinsic magnetic field of the electrons and its alignment by an external field. The fine and hyperfine structures were found in this way. Only the interpretation was too demanding. The spin is a phenomenon of magnetic dipole moment of subatomic particles, not a separate entity.

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  • $\begingroup$ Really nice answer. Here is an interesting one: physics.stackexchange.com/questions/568542/… $\endgroup$ – Árpád Szendrei Aug 1 at 16:36
  • $\begingroup$ Fascinating answer. It begs the related question, why is the electron intrinsically an electric monopole and a magnetic dipole (and not a magnetic monopole as well)? $\endgroup$ – Mathews24 2 days ago

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