# Response of a loop of current vs. a rigidly rotating charged ring to a magnetic field

In a uniform magnetic field, a loop of current on a wire will feel a torque that makes the magnetic moment of the loop align with the field direction. But for a rigidly rotating ring of charge, its magnetic moment will Larmor precess about the direction of the magnetic field (at a rate given by its gyromagnetic ratio).

How and why does this difference arise? In both cases, the loops have a magnetic moment and net angular momentum, and both of these vectors are normal to the plane of the loop. It seems that either both or neither setups should exhibit precession.

• > "a loop of current on a wire will feel a torque that makes the magnetic moment of the loop align with the field direction" Why do you think that? I think a free floating current carrying ring (wire) may show precession as well. Unless there is enough friction or other external forces to make the precession go away and then the magnetic moment will align with external magnetic field. Commented Feb 21, 2023 at 23:14
• @JánLalinský because all the discussions of this specific problem in textbooks and articles say so. For example the problem of the torque on a square loop of current is found by calculating the force on each side and you see the loop will turn parallel to B, exactly the way an electric dipole will turn parallel to E. It doesn't precess. That said, I think you are right and this example neglects the angular momentum the flow of current causes on the loop. But I am struggling to understand how to make that issue clear and precise to be fully convinced. Commented Feb 21, 2023 at 23:33
• I think in most textbooks they don't go to such detail on purpose, and denial of precession in those textbook examples can be made correct by an additional assumption, that the current loop is constrained by some hinges, so it can rotate around one axis, but not around other axes, so precession is prevented. Commented Feb 21, 2023 at 23:50
• @JánLalinský perhaps, but I feel like that sort of constraint is usually explicitly stated. I might be more willing to accept the idea that they only intend to give the instantaneous torque and that how the system evolves in time depends on additional inputs/initial conditions. For example, the current carrying wire could also be rigidly rotating in the reverse direction to exactly cancel the angular momentum of the current carriers, in which case I believe no precession would be the correct motion. In the rigidly rotating case, this sort of freedom doesn't exist, so precession is mandatory. Commented Feb 22, 2023 at 0:07
• @heranias any new ideas? I came up with the same question studying proton precession... Commented Oct 8, 2023 at 19:55