# Accelerating a Magnetic dipole through a uniform magnetic field

If an (uncharged) magnetic dipole travels through a uniform magnetic field with uniform velocity perpendicular to the direction of the B field (lines) it experiences no force. But if I somehow ACCELERATE the magnetic dipole through the same uniform B field will it experience in its frame a magnetic field gradient and therefore experience a force? IOW, under acceleration does it see a spatial gradient dB/dr...and thus experience a force in the direction of the neg. gradient. And if so, can someone derive or supply the equation of motion please. Thanks.

I could give you an answer only for such elementary particles like neutron and electron.

Lorentz force for electrons

From yor question it seems clear that you are familiar with this phenomenon. To go over to the neutrons behaviour first I have to explain to you what is the mechanism behind this deflection.

Perhaps you know that electrons have an intrinsic magnetic dipole moment and a parallel to this moment itrinsic spin. If an electron is under the influence of an external magnetic field the electrons magnetic dipole moment gets aligned.

If this happens with a moving (no parallel to the external field) electron the gyroscopic effect takes place and the electron gets deflected sideways. But any deflection is in physics an acceleration and since we observed many times, an acceleration is accompanied with the emission of photons. Photons have momentum and the emission from the electron dissalign the electrons magnetic dipole moment again. The game starts again until the electron came in rest to the external magnetic field.

Force on a neutron from an external magnetic field

What is the difference between a neutron and an electron? The neutron has no electrical charge and the values of the intrinsic spin and the magnetic dipole moment are different (but existing!). To make a experiment with neutrons is more difficult due to their production and their high velocity as well as their approx. 1000 times - in comparison to the electron - mass. But due to the neutrons intrinsic properties and kinetic energy it will be deflected in an external magnetic field.