# Magnetic force applied to electron spin magnetic moment

by sweet springs
Tags: applied, electron, force, magnetic, moment, spin
 P: 449 Hi The magnetic force applied to electron spin magnetic moment is interpreted by Lorentz force qvXB ? I do not think so. If not, we easily understand why magnetic force can work. Regards.
 P: 449 Please find attached Figure for your understanding of the case. permanent magnet ●●●●●○○circle current equivalent to electron spin magnetic momentum ●●●N●○○○○○●○ ●●●N●○○○○S●N○→Z　direction ●●●N●○○○○○●○↓ ●●●●●○○○○○○○Y direction ○○○○○○○○○○○○ Attractive force can be interpreted as Lorenz force? Regards.
 P: 449 Velocity of part of charged ring is 　ｖ＝　ｖ_xy velocity of rotation ＋　v_z velosity of approach v_z=0 at t=0. 　B from magnet is spreading through the ring, so sum of F＝ｑ（ｖXB)＝　ｑ( ｖ_xy X B) is the attractive force to the magnet. After some time 　F＝ｑ（ｖXB)＝　ｑ( ｖ_xy X B) + ｑ( ｖ_z X B) The second term try to reduce the current rotation. In other words, induced electric field appears as magnetic flux through the ring increase. Quantum rule prohibits reducing speed of spin of electron, so the second term does not apply to the electron spin. Thus the work done by magnetic force to the electron spin is dW = F・v = F・v_xy≠０　　 Magnetic force can work on charged particle with spin. Is the above discussion all right? Regards.
 Sci Advisor PF Gold P: 1,777 Magnetic force applied to electron spin magnetic moment I seem to recall that the spin of the electron when interpreted literally would require the electron to spin faster than c. It isn't meant to actually mean that the electron is spinning. It is simply a property of the electron that we choose to call "spin" because it has quantum mechanical analogs to the spin in classical mechanics. It is enough to note that the spin of the electron gives it a weak magnetic moment. We can use this moment to interpret the energy and forces that the electron undergoes in a magnetic field. Even more explicitly, you can just use the actual field excited by the dipole. Either way, we do this in many cases like in the hyperfine splitting of the hydrogen atom which arises due to the spin-spin coupling of the electron and proton from the interaction of the magnetic fields that arise from their spin. Of course, this is in addition to any forces that acts on the charge from a magnetic field acting on it due to its movement and there can also be an orbital magnetic moment that also arises.
 P: 449 Hi. Born2bwire Thank you so much. I will restate your teachings to confirm my understanding Interaction energy of spin magnetic moment m and magnetic flux density B is 　　U＝-m・B . The force applying to the electron is 　－∇U＝∇(m ・B). These are very fundamental law that we cannot describe it by Loretz force F=qvXB. The force is free from not-do-work law of F・v=0. It may apply for not only spin but quantized orbit motion of electron. Now I understand why attractive force between two magnets do work. Regards.
PF Gold
P: 1,777
 Quote by sweet springs These are very fundamental law that we cannot describe it by Loretz force F=qvXB. The force is free from not-do-work law of F・v=0.
I don't know if I would go as far as that. Basically, we cannot say how the magnetic moment is produced. In classical physics, magnetic fields are produced only by moving charges and thus we can say that for classical electrodynamics magnetic fields do no work. We can model the magnetic moments of atoms as microscopic loop currents. But with the actual quantum model, we could, in a hand wavy kind of way, say that the orbital moment is the equivalent of the loop currents and this does play a hand in what I think is diamagnetism. Paramagnetism is the magnetic fields related to the moments from the particles' spin. However, since we do not have a true picture for what spin is or how it produces the moment, I do not think we should go as far to say that it is free from the restrictions of the Lorentz force.

If the electron is in motion, like it is with an atom, then the electron will see a transformed set of fields according to the Lorentz transformations (well, more complicated than that since the electron in an atom is an accelerating frame of reference if we can even dare to think of it in such a definite way). That means that a static magnetic field in the lab frame can have an electric field in the frame of motion. So the electron itself can see a static electric field which can do work via the Lorentz force.

But I think it all comes down to what is the actual property of spin. A literal idea would be that the electron is a charged shell that is spinning which we then can easily use the same arguments to show that there is no work being done by the magnetic fields. But we can't say that this is true. In the end, it is probably best to leave it as an open question. Not to mention that we are trying to cherry pick quantum ideas and put them into the classical universe. We can use quasi-quantum models to generate good results but I think it is instructive to remember that the physics in the classical and quantum world are different.
 P: 449 Hi. Born2bwire. Set of magnets attract or repel and do work obviously. It is not easy at least for me to explain this by Lorenz force which do not work. This is the motivation I imagined above, but I should treat this more thoughtfully. Thank you so much.