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In the Larmor precession, we tend to define the magnetic moment as the current multiplied by the surface (for an electron rotating around a nucleus), sometimes this moment is defined (generally) as the sum of the vectoriel products of half of the position vector and the charge times the velocity. But once we apply a magnetic field for the case of a unique electron, the "magnetic moment" starts rotating around the z-axis and the trajectory of the electron is no longer a circle. Now the obvious thing is that there is no average "current", because there is no loop (the electron starts to move in a quite different circular paths and never comes back to an earlier position), so the definition of the magnetic moment that uses the current is not correct in the Larmor precession, unless we consider that the electron period of rotation around the nucleus is negligible with respect to the Larmor period, which gives quite the same trajectory when there is no magnetic field. The problem in general is, are we still allowed to use the magnetic moment in, the Newton second law (the moment appears in the couple) and then deduce the famous larmor equation by substituting the angular momentum by the gyromagnetic relation? And what is the exact definition of the magnetic moment?

To sum up, do you think that there are some circumstances (time scale for example) at which there is a problematic in the Larmor equation that gives the precession the magnetic moment?

Thank you,