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So I was just reading a bit about magnetic dipole moments, Larmor precession, angular momentum etc., but there was one little thing that was bothering me. As far as I know, any angular momentum will precess around any magnetic field, no matter how big the angular momentum and the magnetic field is. So the angular momentum can be as small as you like. So then I thought about bar magnets, which I thought had a very tiny amount of angular momentum due to their magnetic dipole moments, for as we know, the magnetic dipole moment is the gyromagnetic ratio (gr) times the angular momentum. But of course, the gr is really big for bar magnets because it's so large for electrons (and as we know, it is the electrons that make up the currents that are creating the magnetic field of the magnet). Thus, the angular momentum of bar magnets must be microscopically small. But again, as I said, any angular momentum will do, meaning that bar magnets should actually precess. What is wrong with my thinking here?

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The magnetization in a bar magnet is due to the alignment of the spin magnetic moments of the electrons, not to currents. The precession would depend on the cross product $\mu\times{\bf B}$. Since $\mu$ is aligned along $\bf B$, there is no torque and no precession.

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  • $\begingroup$ Yeah, that is what happens when the bar magnet has already aligned with the magnetic field. I wonder what happens before it has aligned. As I said, the bar magnets should actually precess around the field due to the torque, just as current loops with angular momentum do. $\endgroup$ – Felis Super Jul 16 at 7:35
  • $\begingroup$ I thought you were asking if the bar magnet would precess due to its own magnetic moment and angular momentum. If $\mu\times{\bf B}$ Is not zero, there will be a torque. The magnet would precess if it had a large angular momentum, but if the angular momentum is small (as in the case of a bar magnet), it would just rotate to align with the magnetic field as a compass needle does. A gyroscope precesses is because it has a very large angular momentum. $\endgroup$ – Jerrold Franklin Jul 16 at 9:50
  • $\begingroup$ Right, but I wanna know why. As I explained in the question, it seems like Larmor precession should occur no matter how big the angular momentum is. I mean, I have never heard of any lower limit on the angular momentum for precession to work. Therefore, it seems like bar magnets should precess due to their tiny amount of angular momentum. $\endgroup$ – Felis Super Jul 16 at 10:03
  • $\begingroup$ Applying torque to a 'rotating' object is a complicated subject. In the case of a magnet, the original angular momentum comes from the spin of the aligned electrons. When a torque is applied, two things can happen. One is precession, which concerns you. The other is that the object acquires additional angular momentum by just falling over. $\endgroup$ – Jerrold Franklin Jul 16 at 13:38
  • $\begingroup$ You can see what happens if you spin a toy top. As it starts to slow down, it first wobbles, which is a sign of precession. Then as it goes slower with less angular momentum, it falls over. The bar magnet is like the top with so little angular momentum that it just falls over. Before we continue, you should read up about procession, but it will be very difficult reading. $\endgroup$ – Jerrold Franklin Jul 16 at 13:38
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If the object precesses or not, or does something inbetween, namely nutate, depends on the ratio of Larmor frequency to the rotation frequency of the object. If you start from a situation where the magnet is tilted with respect to the field and then you let go, you obtain perfect precession only, if the rotation frequency is infinite. One may think of electrons, which are point-like with zero moment of inertia, as having infinite rotation frequency for their finite angular momentum of hbar/2. For any object with a spatial extent and non-zero moment of inertia, the transition from perfect precession to "swinging" is gradual, depending on the size of angular momentum and thus rotational frequency.

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