Question about a magnetic dipole in an inhomogeneous magnetic field.Please help

In summary, the Stern Gerlach experiment does not mention torque because the inhomogeneity of the magnetic field can cause significant deflection before much rotation takes place. In the classical view, this is due to the particle passing through a changing field and not having time to align with any field lines. In the quantum mechanical explanation, the static magnetic field does not allow for spin flips, and the deflection depends on the dipole's magnetic moment vector. The inhomogeneity refers to the strength of the magnetic field in the z direction, not just the direction of the field lines.
  • #1
alfredblase
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Take the example of a magnetic dipole in a magnetic field. The dipole will experience a torque that will tend to align its magnetic moment with the field lines of the magnet. So why on Earth is there no mention made of this torque in any of the countless descriptions of the Stern Gerlach experiment I have read??! All the diagrams and applets I have seen show the magnetic dipole passsing through the field experiencing only deflection and no rotation! I am tearing my hair out over this one, am I missing something?! :cry:
 
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  • #2
Your question has to be answered twice. First, classically (which doesn't really apply, but that wasn't known until after the experiment):
The inhomegenity 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
 
  • #3
Meir Achuz said:
The energy difference between the two states is [tex]\Delta E=2B\cdot\mu[/tex]. The spin can only be flipped by an oscillating magnetic field of frequency [tex]\hbar\omega=\Delta E[/tex]

Thanks for your reply. Just thought i'd quote with the equations showing in tex. Still not sure I understand exactly how (in the classical view) increasing inhomogeneity decreases the amount of rotation. Would I be right in saying that because the dipole is moving and passing through an effecctively random changing field it never has time to align itself with any field lines? But in all diagrams I have seen the shape of the magnets is the same all allong the path of the beam and therefore it would be as if the dipole had been in a particular B field all through its path and so it would be rotated regardless of the inhomogeneity along the axis perpendicular to its path... I guess I don't understand.
 
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  • #4
Actually I think I see now. What is meant by inhomogeneity is not necessarily about the diretion of the field lines but more about the increasing strength of the field in the z direction. If this gradient is made large enough the dipole will be deflected significantly by this magnetic gradient before it has time to rotate much, and the deflection vector depends upon the dipole magnetic moment vector. =)
 
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1. What is a magnetic dipole?

A magnetic dipole is a magnetic object or system that has two opposite poles, a north pole and a south pole, with a magnetic field extending from one pole to the other. This is similar to an electric dipole, but instead of positive and negative charges, there are north and south magnetic poles.

2. What is an inhomogeneous magnetic field?

An inhomogeneous magnetic field is a magnetic field that varies in strength and direction at different points in space. This means that the magnetic field is not uniform and can have different values at different locations.

3. How does a magnetic dipole behave in an inhomogeneous magnetic field?

A magnetic dipole will experience a torque, or rotational force, when placed in an inhomogeneous magnetic field. The direction and magnitude of the torque will depend on the orientation of the dipole and the strength of the magnetic field at different points.

4. What is the formula for calculating the torque on a magnetic dipole in an inhomogeneous magnetic field?

The formula for calculating the torque on a magnetic dipole in an inhomogeneous magnetic field is τ = μ x B, where τ is the torque, μ is the magnetic dipole moment, and B is the magnetic field vector. This formula is based on the cross product between the dipole moment and the magnetic field.

5. Can a magnetic dipole be in equilibrium in an inhomogeneous magnetic field?

Yes, a magnetic dipole can be in equilibrium in an inhomogeneous magnetic field if the torque on the dipole is equal to zero. This can occur when the dipole is aligned with the magnetic field or when the magnetic field is symmetrical around the dipole. In these cases, the dipole will not experience any rotational force and will remain in a stable position.

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