Given the magnetic dipole moment in external uniform magnetic field $\vec{B}$, I am trying to understand why sometimes $\vec{\mu}$ simply aligns with the $\vec{B}$ and stays that way, while other times $\vec{\mu}$ starts precessing around $\vec{B}$?

I am interested in both the classical and the quantum concepts of this phenomenon. When I read quantum physics books it seems to me that in quantum world we always have precession and never simple alignment (interaction between say electron spin and external field):

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while in classical world we sometimes get one and other times the other.

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Is there some condition for precession? I am looking for an intuitive answer just to get some picture/concept in my head, not strict mathematical explanation.

  • $\begingroup$ The dipole does indeed precise. In classical mechanics, we only approximate its allignment for simplification. This is only valid if the dipole turns quasistatically whrn B is switched on(hypothetical situation) $\endgroup$ – Lelouch Jul 5 '16 at 0:12

I want to give an answer for electrons which have both an intrinsic spin and a magnetic dipole moment. The key for the understanding why electrons in rest in relation to an external magnetic field get aligned and do not precess while moving non-paralle to the external magnetic field electrons undergo a precession is their kinetic energy in relation to the external field.

Electron in rest

An electron in rest when under the influence of a static magnetic field will get aligned with its magnetic dipole moment. For this case nothing more happens, there is no acceleration of the electron nor emission of EM radiation.

Electron in motion in relation to an external magnetic field

There is a well known macroscopic effect of the precession of a rotating wheel, called the gyroscopic effect. On the electrons level this effect can be explained as follows. Underthe influence of the external magnetic field the electron gets aligned with its magnetic dipole moment and by this a small amount of the kinetic energy gets converted into EM radiation. This is what we observe. Emitting photons the electron gets disaligned again. The photons momentum has to be compensated by the movement of the electron and by this the electron gets deflected from its straight trajectory. Once disaligned the game starts again and again. The resulting trajectory is not only a spiral path lasting until the electron is in rest with the external magnetic field and has exhausted its kinetic energy, but the trajectory in detail is made of tangerine slices.

  • $\begingroup$ so if I get it right, if electron is at rest then it will only align to the external field, but if electron is moving then we have precession? In other words, precession happens only for moving charges? $\endgroup$ – matori82 Oct 3 '16 at 15:06
  • $\begingroup$ @matori82 Exact. You get it. $\endgroup$ – HolgerFiedler Oct 3 '16 at 15:29

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