Force exerted on iron particle in a magnetic field

Question

So when an iron particle is near a permanent magnet. We see that iron particles will be attracted to the magnet and the iron particle will experience a force directed towards the north or south; is it possible to calculate the acceleration and time taken to reach the magnet.
Is this force quantifiable?
I don't think a charged particle in magnetic field equations will work as this is an example of ferromagnetism.

R.W. Bird · Answer

The field from the magnet produces a magnetization within the particle which depends on its susceptibility and the field strength (which varies with position outside of the magnet). The magnetization is the dipole moment per unit volume. Knowing the volume of the particle, you get its dipole moment. Then the force on the particle is its dipole moment times the gradient of the field (which also varies with position). (The dipole moment is also subject to a torque which aligns it with the field.)

Answered by R.W. Bird on October 4, 2021

Force exerted on iron particle in a magnetic field

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