Deflection of a Magnet in an Inhomogenous Magnetic Field

[Hornbein]

Say I've got a magnet flying through empty space in a homogenous magnetic field. The magnet precesses and flies in a straight path. Now make that magnetic field inhomogenous. The magnet precesses and flies in a curved path. What I can't figure out is why the path is curved. It is because the precession force is stronger on some parts of the magnet as compared with others. But why does this affect the path of the magnet as a whole? I wrongly think it should only cause a wobble or something like that, not change the momentum of the object as a whole.

 

[hutchphd]

In an external field the dipoles will tend to orient along the field. It the field is uniform the dipole is equally repelled and attracted. It there is a gradient, one end of the dipole will be pulled harder than the other is repelled (or vice versa). The generalization to continuous media is obvious I think.

 

[Hornbein]

In an external field the dipoles will tend to orient along the field. It the field is uniform the dipole is equally repelled and attracted. It there is a gradient, one end of the dipole will be pulled harder than the other is repelled (or vice versa). The generalization to continuous media is obvious I think.

Thanks to you I see why the flight path is no longer straight. Now let's see if I have this right. The magnet will continue to precess, so the direction of the force will not be constant. The path will be a helix?

 

[hutchphd]

The dipoles, if they have angular momentum as well (this is NMR ?), will precess about the flux lines at a rate proportional to the local field strength. In addition they will be attracted towards stronger field as I described. The path of the center of mass of the dipole will not be helical...it will be pulled directly toward the regions of stronger field. This will not generally be along the flux lines

 

[Hornbein]

The dipoles, if they have angular momentum as well (this is NMR ?), will precess about the flux lines at a rate proportional to the local field strength. In addition they will be attracted towards stronger field as I described. The path of the center of mass of the dipole will not be helical...it will be pulled directly toward the regions of stronger field. This will not generally be along the flux lines

Oh now I get it. It's just a magnet attracting/repelling another magnet. Now let me check if I have this right. The orientation of the free magnet will be a complicated function that depends on the flux lines of the field combined with precession of the poles.

 

[vanhees71]

If you have a magnetic dipole the force is given by the potential
$$V=-\vec{m} \cdot \vec{B} \; \Rightarrow \; \vec{F}=\vec{\nabla} (\vec{m} \cdot \vec{B}).$$
The torque is
$$\vec{\tau}=\vec{m} \times \vec{B}.$$