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In the book "Introduction to Electrodynamics, 4th edition" by Griffiths, the author says, I quote from page 278 :

(...) We call it a "bound" current to remind ourselves that every charge is attached to a particular atom, but it's a perfectly genuine current, and it produces a magnetic field in the same way any other current does. (...)

Basically what he explains in that section is that the magnetic dipole moment of every electron in a magnetized material contribute to an overall surface current (much like the rollers in a conveyor belt) and it is this current that produces the magnetic field around the material.

It seems to me however that these surface currents are not brought up in most descriptions of magnets. For example, in this video :

MAGNETS: How Do They Work?

it is explained that the magnetic field produced by a magnet is a quantum phenomena that arises because electrons have a quantum property called intrinsic magnetic moment.

Question : Are these surface currents really genuine currents? Do we have any evidence for their existence? Or is it just a model that is used in calculations but does not reflect reality?

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  • $\begingroup$ Nice made video. Unfortunately it is has a weakness. It is explained that electrons obey an intrinsic (existing independent from outer conditions or changes) magnetic dipole moment. Why it is needed to talk further about the movement of this electrons and that the resulting current bear magnetic fields? An macroscopic magnetic field is simply induced by the alignment of the magnetic dipole moments of the involved electrons. $\endgroup$
    – HolgerFiedler
    Commented Aug 25, 2017 at 15:56
  • $\begingroup$ I saw this video recently : How Special Relativity Makes Magnets Work and I wanted to know if there was an alternative way of thinking about how magnets attrack each other but only in terms of electric fields. I find it extremely beautiful to think of a piece of magnet as having a current flowing on its surface (and in its volume) so that when two magnets are close to each other, electricity and special relativity makes the magnets attrack or repel. I am wondering however, if those surface currents really are genuine in the sense that they exists. $\endgroup$
    – Corvinus
    Commented Aug 25, 2017 at 18:48

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There is a concept in electrodynamics that, outside a physical volume, that the resulting fields can be given by the fields outside a surface with currents and charges on that surface. This is a Green's Function (See Wikipedia Green's Function for more information).

Whether one attributes the calculated fields to volume currents or surface currents—in each case, one should get exactly the same result, when everything is calculated properly. So one could view the result as genuine surface currents as the source of the resulting fields. Or genuine volume currents. It is kind of like the question of a Heliocentric solar system or an Earth-centric solar system. Which is right? Well, one is just a coordinate transformation of the other. The physical laws, when transformed from the one coordinate system to the next, give the resulting values from the calculated perspective.

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  • $\begingroup$ Correct me if I am mistaken but aren't you suggesting that, as long as two models calculate the same thing, it is undecidable which one is right, i.e. reflects reality? Every model used in calculations does not necessarily reflect reality. For example, in electrostatics, one can apply the method of image charges to calculate fields more easily in some problems, but the added charges are just imaginary, they are not real. What I mean by real is that : are they measurable/observable? $\endgroup$
    – Corvinus
    Commented Aug 24, 2017 at 21:01
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    $\begingroup$ Just like if one sees an image in a mirror, one can attribute the image to something that has a three dimensional effects on one's understanding, or one can look at the reflection as surface currents, these are similarly two models that from the outside of the boundary result in the same result. $\endgroup$
    – Stephen Elliott
    Commented Aug 28, 2017 at 14:40
  • $\begingroup$ Tip: Note that salutations are discouraged on SE. $\endgroup$
    – Qmechanic ♦
    Commented Aug 28, 2017 at 20:49

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