I'm struggling to understand how to calculate the force exerted on an uncharged particle in a magnetic field. Consider the following setup: a ball of ferromagnetic iron weighing 1kg is placed in a uniform magnetic field of 1 Tesla. What is the force exerted on the iron ball?
Most of the information I've found so far is limited to charged particles in magnetic fields, which results in the textbook helical motion. However, uncharged particles (such as an atom of iron) also clearly show an attraction toward magnets. What equation can I use to relate the strength of the magnetic field to the force exerted on an uncharged particle suspended in it?
A similar situation for electric forces would use $F=qE$, but there's no charge on an atom of iron so I'm not sure what to use.