Magnetic force applied to electron spin magnetic moment

  1. Hi
    The magnetic force applied to electron spin magnetic moment is interpreted by Lorentz force qvXB ? I do not think so. If not, we easily understand why magnetic force can work.
  2. jcsd
  3. Please find attached Figure for your understanding of the case.

    permanent magnet
    ●●●●●○○circle current equivalent to electron spin magnetic momentum
    ●●●N●○○○○S●N○→Z direction
    ●●●●●○○○○○○○Y direction

    Attractive force can be interpreted as Lorenz force?
  4. Velocity of part of charged ring is
     v= v_xy velocity of rotation + v_z velosity of approach

    v_z=0 at t=0.  B from magnet is spreading through the ring, so sum of F=q(vXB)= q( v_xy X B) is the attractive force to the magnet.

    After some time

     F=q(vXB)= q( v_xy X B) + q( v_z X B)

    The second term try to reduce the current rotation. In other words, induced electric field appears as magnetic flux through the ring increase.

    Quantum rule prohibits reducing speed of spin of electron, so the second term does not apply to the electron spin.

    Thus the work done by magnetic force to the electron spin is
    dW = F・v = F・v_xy≠0  
    Magnetic force can work on charged particle with spin.

    Is the above discussion all right?
  5. Born2bwire

    Born2bwire 1,776
    Science Advisor
    Gold Member

    I seem to recall that the spin of the electron when interpreted literally would require the electron to spin faster than c. It isn't meant to actually mean that the electron is spinning. It is simply a property of the electron that we choose to call "spin" because it has quantum mechanical analogs to the spin in classical mechanics.

    It is enough to note that the spin of the electron gives it a weak magnetic moment. We can use this moment to interpret the energy and forces that the electron undergoes in a magnetic field. Even more explicitly, you can just use the actual field excited by the dipole. Either way, we do this in many cases like in the hyperfine splitting of the hydrogen atom which arises due to the spin-spin coupling of the electron and proton from the interaction of the magnetic fields that arise from their spin. Of course, this is in addition to any forces that acts on the charge from a magnetic field acting on it due to its movement and there can also be an orbital magnetic moment that also arises.
  6. Hi. Born2bwire
    Thank you so much.

    I will restate your teachings to confirm my understanding

    Interaction energy of spin magnetic moment m and magnetic flux density B is
      U=-m・B .
    The force applying to the electron is
     -∇U=∇(m ・B).

    These are very fundamental law that we cannot describe it by Loretz force F=qvXB.
    The force is free from not-do-work law of F・v=0.
    It may apply for not only spin but quantized orbit motion of electron.

    Now I understand why attractive force between two magnets do work.

  7. Born2bwire

    Born2bwire 1,776
    Science Advisor
    Gold Member

    I don't know if I would go as far as that. Basically, we cannot say how the magnetic moment is produced. In classical physics, magnetic fields are produced only by moving charges and thus we can say that for classical electrodynamics magnetic fields do no work. We can model the magnetic moments of atoms as microscopic loop currents. But with the actual quantum model, we could, in a hand wavy kind of way, say that the orbital moment is the equivalent of the loop currents and this does play a hand in what I think is diamagnetism. Paramagnetism is the magnetic fields related to the moments from the particles' spin. However, since we do not have a true picture for what spin is or how it produces the moment, I do not think we should go as far to say that it is free from the restrictions of the Lorentz force.

    If the electron is in motion, like it is with an atom, then the electron will see a transformed set of fields according to the Lorentz transformations (well, more complicated than that since the electron in an atom is an accelerating frame of reference if we can even dare to think of it in such a definite way). That means that a static magnetic field in the lab frame can have an electric field in the frame of motion. So the electron itself can see a static electric field which can do work via the Lorentz force.

    But I think it all comes down to what is the actual property of spin. A literal idea would be that the electron is a charged shell that is spinning which we then can easily use the same arguments to show that there is no work being done by the magnetic fields. But we can't say that this is true. In the end, it is probably best to leave it as an open question. Not to mention that we are trying to cherry pick quantum ideas and put them into the classical universe. We can use quasi-quantum models to generate good results but I think it is instructive to remember that the physics in the classical and quantum world are different.
  8. Hi. Born2bwire.

    Set of magnets attract or repel and do work obviously.
    It is not easy at least for me to explain this by Lorenz force which do not work.

    This is the motivation I imagined above, but I should treat this more thoughtfully.

    Thank you so much.
  9. Born2bwire

    Born2bwire 1,776
    Science Advisor
    Gold Member

    Threads along these lines have been popping up a lot latey. In essence, it comes down to the fact that fiels undergo Lorentzian transformations under all conditions. If we see only a static magnetic field when we are at rest, then if we observe the same field while in motion, we can see a magnetic and electric field. What happens is that the magnetic fields only act upon moving charges. Thus, if we were to transform to the frame of the charge, we will see a transformed magnetic field. The transformation will create an electric field that can do the work. I think one way to look at it is that we can extract energy from magnetic fields, but to do this we have to use electric fields to mediate the exchange of energy/work. Showing this in an actual problem is a very complicated matter. The case of two current carrying wires is a common case done in texts like Griffiths and Purcell. In those texts, they show that the magnetic force that acts on the wires can be seen as an electric force from the charge's perspective. In addition, Griffiths has some further explanation by stating that you can also think of the magnetic field as being a way of redirecting the electric force. In this case, you can think of a magnetic field acting on a current carrying wire and Griffiths demonstrates that the magnetic field redirects the direction of the force on the current carriers that is being applied by the voltage source of the wire.

    All this holds true for classical electrodynamics. It's in quantum that we start to see sources of fields that do not arise from charges alone. Photon emission from atoms, the vacuum fields, and the magnetic moment from a charge's spin are examples of quantum sources of fields that have no classical explanation. However, I do not think you need to introduce such ideas to work around how or how not a magnet can do work as these ideas are soley borne out of classical electrodynamics.
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