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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.

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  • $\begingroup$ 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
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Classically, the magnetic potential energy is $U=-\boldsymbol{\mu}\cdot\textbf{B}$. Energy is conserved. Therefore if there is no mechanism for dissipation or for exchanging potential energy for kinetic energy, the angle between the two vectors has to stay the same. If you take a bar magnet and hang it from a string, then it can precess in the earth's field, or just keep its original orientation, or oscillate, depending on the initial state of rotation. If it's oscillating, then there is an interchange of kinetic and potential energy. In a hiking compass, it will oscillate, but there is strong damping because it's water filled, so the energy is dissipated rapidly into heat, and the needle ends up aligned with the field.

Quantum-mechanically, there really isn't any concept of precession for a microscopic body. For example, suppose an electron is in a magnetic field that's in the $z$ direction. Say we put the electron in a state of definite energy. Since there is no dissipative mechanism and no way to exchange PE with KE, the electron must have constant $\boldsymbol{\mu}\cdot\textbf{B}$, i.e., $\mu_z$ stays constant. But in this situation $\mu_x$ and $\mu_y$ are completely uncertain, so it doesn't make sense to imagine the moment as a vector that's precessing.

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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.

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  • $\begingroup$ 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. $\endgroup$ Oct 3 '16 at 15:29
  • $\begingroup$ This just sounds wrong. This has nothing to do with whether the electron is moving or not, unless you mean something about Thomas precession, and what you're saying doesn't sound like a correct description of at at all. $\endgroup$
    – user4552
    Oct 30 '19 at 20:02
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I don't think the interpretation of HolgerFiedler is correct, or I really don't understand why. I feel there is a confusion between "motion", angular momentum and magnetic moment...

I am more satisfied with this interpretation I have found on https://www.physicsforums.com/threads/question-about-a-magnetic-dipole-in-an-inhomogeneous-magnetic-field-please-help.109669/

Your question has to be answered twice. First, classically (which doesn't really apply, but that wasn't known until after the experiment): The inhomogeneity can be made large enough so that there is significant deflection before much rotation takes place. You can see what is needed from the equations. You would have to assume a classical moment of inertia of the neutral particle.

Since QM is needed, this classical explanation is really irrelevant. The QM explanation: The particle (if spin 1/2) can only be either up or down in the direction of the B field. The energy difference between the two states is \Delta E=2B\cdot\mu. The spin can only be flipped by an oscillating magnetic field of frequency \hbar\omega=\Delta E. The field in the SG experiment are static, so no spin flip takes place

Classically, I think that the precession can have a really fast response, while for the rotation to occur, some momentum has to be evacuated, through damping (in the case of the electron, radiation maybe). In the case of magnets, I am not really sure how and where the angular momentum goes so fast, but I have never observed any macroscopic precession...

Edit: In the case of the big magnet, all the moments probably try to precess but are blocked because they prefer to stay aligned (shape anisotropy), it's like infinite damping, and the magnet just experiences a torque leading to its alignment along the field. Maybe the magnetic moment is converted into angular momentum via Einstein–de Haas effect, but numerically the angular momentum is too weak to be observed?

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