Magnetic force applied to electron spin magnetic moment

In summary: The problem is that the Lorentz force is not a fundamental force. It is simply the electrodynamic force as viewed from a different frame. It is the same force that we get when we use the magnetic force in the Lorentz transform.In summary, the conversation discusses the interpretation of the magnetic force on electron spin magnetic moment and its relation to the Lorentz force. It is noted that the Lorentz force may not fully explain the attractive force between magnets and that this is an area that requires further thought and consideration. Additionally, the concept of spin and its relation to magnetic moments and classical mechanics is discussed, with the conclusion that it is best to leave the question open for further exploration. The role
  • #1
sweet springs
1,223
75
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.
Regards.
 
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  • #2
Please find attached Figure for your understanding of the case.

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

Attractive force can be interpreted as Lorenz force?
Regards.
 
  • #3
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?
Regards.
 
  • #4
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.
 
  • #5
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.

Regards.
 
  • #6
sweet springs said:
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.

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.
 
  • #7
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.
 
  • #8
sweet springs said:
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.

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.
 

1. What is the concept of electron spin magnetic moment?

The concept of electron spin magnetic moment is a property of electrons that results from their intrinsic spin. It is a quantum mechanical phenomenon in which electrons behave like tiny magnets, with a north and south pole, and can interact with external magnetic fields.

2. How does magnetic force applied to electron spin magnetic moment affect the electron's behavior?

Magnetic force applied to electron spin magnetic moment can cause the electron to align its spin either parallel or anti-parallel to the external magnetic field. This alignment can result in different energy levels for the electron, leading to changes in its behavior and properties.

3. Can magnetic force applied to electron spin magnetic moment be used to manipulate electron behavior?

Yes, magnetic force applied to electron spin magnetic moment can be used to manipulate the behavior of electrons. By controlling the direction and strength of the magnetic field, scientists can control the alignment of electron spin and therefore manipulate the electron's energy levels and interactions with other particles.

4. What are some practical applications of understanding the magnetic force applied to electron spin magnetic moment?

Understanding the magnetic force applied to electron spin magnetic moment has many practical applications, including in the development of magnetic storage devices, such as hard drives, and in the field of spintronics, which uses the spin of electrons for information processing. It also plays a crucial role in many medical imaging techniques, such as MRI.

5. How does the magnetic force applied to electron spin magnetic moment differ from the magnetic force applied to the overall magnetic moment?

The magnetic force applied to the overall magnetic moment is due to the combined effect of both the electron's spin and its orbital motion. On the other hand, the magnetic force applied to electron spin magnetic moment only considers the electron's intrinsic spin. This means that the two forces can have different effects on an electron's behavior and properties in the presence of a magnetic field.

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