Narrow external magnetic field poking through a disk magnet

[particlezoo]

Let's say I have a disk magnet that is a centimeter thick and 1 meter in diameter. Now let's apply an external field confined to a cylinder of arbitrary position, angle, and length. Let's say it has a diameter of << 1 meter, so very, very narrow. Let's presume that the external field lines are closed outside this cylinder with return paths that too far from the disk magnet to affect it.

The questions I ask below pertain to the force on the disk magnet only:

1) Is the force density by this external magnetic field on the disk magnet that of Lorentz force densities on "equivalent sheet currents" on the perimeter of the disk magnet?

2) Or is the force density equivalent to that of what would be experienced by magnetic monopoles spread across each circular face of the disk?

If the former (1) were the case, I would imagine situations where there was no external magnetic field interacting with the "equivalent sheet currents" at the perimeter of the disk magnet, and the result would be no force on the magnet despite the obvious possibility of dipole coupling energy that would be a function of the angle between the disk magnet and the applied field.

If the latter (2) were the case, then assuming the applied field were straight, then there would be no net torque, although there would be equal and opposite forces. This would be despite the dipole coupling energy still being dependent on the angle of the magnet with respect to the applied field.

Now let's consider the possibility that the applied field could be confined to a narrow cylinder that is bent in such a way that it "pokes" through one face at one angle and the other face at a different angle. In this case, it would be possible for the latter case (2) to yield a torque that would act on the magnet, a torque that does not appear to show up for the former case (1) under the condition that the applied magnetic field is completely confined to a spot far from the "equivalent current sheets" at the perimeter of the disk magnet.
Kevin M.

 

[eljose79]

Dear Kevin,

Thank you for your interesting forum post. I would like to address your questions and provide some insights into the force on the disk magnet in the scenario you described.

Firstly, in response to your first question, the force density on the disk magnet can indeed be described as the Lorentz force density on "equivalent sheet currents" on the perimeter of the disk magnet. This is because the magnetic field lines from the external field will induce a current on the disk magnet, creating an equivalent sheet of current on its perimeter.

However, it is important to note that this is not the only factor at play. The force experienced by the disk magnet will also depend on the orientation of the magnet with respect to the external field. As you mentioned, there would still be dipole coupling energy involved, which is dependent on the angle between the disk magnet and the external field.

In response to your second question, the force density can also be described as that of what would be experienced by magnetic monopoles spread across each circular face of the disk. This is because the magnetic field lines from the external field will also induce a magnetic moment on the disk magnet, creating magnetic monopoles on each face.

In this scenario, the net torque on the disk magnet would indeed be zero, as the forces on each face would cancel out. However, as you mentioned, if the external field was bent in a way that it pokes through one face at a different angle than the other, there would be a net torque on the disk magnet.

In summary, the force on the disk magnet is a combination of both the Lorentz force density on the equivalent sheet currents and the force experienced by magnetic monopoles on each face. The net force and torque on the disk magnet will depend on the orientation of the magnet with respect to the external field and the specific geometry of the field.

I hope this helps clarify the situation for you. If you have any further questions or would like to discuss this topic further, please don't hesitate to reach out.