When learning about magnetic fields, it is said that stationary charges do not have any effects due to magnetic fields. So when explanations are given, is the spin of the charges not considered? And if an electron (with no linear velocity) is placed in a magnetic field, will it have any effect due to its intrinsic spin?
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$\begingroup$ Have you learned about what external magnetic fields do to a current loop? That is things like torque and potential energy of a current loop in a magnetic field? $\endgroup$– TriatticusCommented Apr 24 at 18:37
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2$\begingroup$ Magnetic fields do couple to the intrinsic (quantum) spin of fundamental quantum mechanical particles like electrons. This is often ignored when learning basic electromagnetism until later, because it's a more complicated effect (requires the coupling a magnetic field to a magnetic dipole). The assumptions at the basic level is often that a particle has intrinsic charge but not spin. We add it in later. $\endgroup$– marchCommented Apr 24 at 18:45
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Quantum spin does affect magnetic fields and is affected by magnetic fields. However, this is a great example of how the theory and reality are two separate things.
In reality, particles have spin. The behavior of the electron depends a lot on the value of its spin, and changing the value of the spin would lead to a wildly different behavior.
However, when dealing with classical electrodynamics, generic charge and current distributions know nothing about spin. The infinitesimal charges used to build up these distributions are scalar charges, without any intrinsic structure or spin. We know that in reality that is not how things work, but this approximation is useful as a model for many realistic scenarios. Quite often the effect due to the electrons' spin will be negligible compared to the other contributions due to the macroscopic arrangements of charges and currents.
To understand spin in classical electrodynamics, a common model, discussed for example in the book by Griffiths, is to picture electrons as tiny loops of current. Since the fundamental charges of electrodynamics are often taken to be scalars, this is the most natural way to implement spin in a simple manner. Alternatively, you could have a distribution with dipoles or something of the sort.
A more nuanced (but more precise) approach is to consider a different field theory. Instead of working with a generic charges and currents, we instead give a precise theory for how these charges and currents should behave. This can come, for example, by asking that they are sourced by the solutions to the Dirac equation, which is the relativistic and quantum mechanical equation ruling the behavior of electrons. In this approach, spin will be intrinsically considered in your model. However, solving this set of equations will be much harder. Quantizing this theory will lead you straight to quantum electrodynamics.
In summary, you are correct: spin is ignored in these explanations. This is due to the fact that while spin does exist in reality, electrodynamics as a theory does not know that the fundamental charges are electrons with spin half. It just assumes a generic charge distribution, that can ignore the effects of spin. A more nuanced model can be made by specifying more details about the dynamics of the charges and currents, but this greatly increases the difficulty of solving the theory.
If my memory doesn't fail me, Griffiths has a nice discussion about spin in classical electrodynamics. I encourage you to check it out. (I mean the electrodynamics book, not the quantum mechanics book).
answered Apr 25 at 1:49
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$\begingroup$ Is magnetism an intrinsic property of matter like electric charge: Why not understand the magnetic dipole of an electron as an intrinsic property in the same sense as the electrons electric field? Why „ To understand spin in classical electrodynamics, a common model, discussed for example in the book by Griffiths, is to picture electrons as tiny loops of current“? $\endgroup$ Commented Apr 26 at 4:26
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$\begingroup$ @HolgerFiedler That is a limitation of Electrodynamics as usually presented, in which we treat the fundamental charges as scalars. I believe treating them as spinors, as they should, would solve the problem, but that is harder and unconventional. The issue is that the theory is just a theory, it doesn't need to capture all properties of reality $\endgroup$ Commented Apr 26 at 14:13
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$\begingroup$ Thank you for your understanding response. However, as an amateur, I keep asking myself whether it's about time that physicists reconsidered their view on the priority of the magnetic dipole of the electron and the spin. It would make physics a lot less complicated. $\endgroup$ Commented Apr 26 at 20:11
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$\begingroup$ It is always difficult to break free from the ivory tower of science. After the next revision of conventions, everything seems completely natural, but before that, the conditioned physicist resists any innovation. I'm over 60 and I'm not giving up hope of living to see the next round of interpretation. More than 100 years have passed since Einstein and Plank's interpretations, so it's getting boring. $\endgroup$ Commented Apr 26 at 20:19