I found it possible that most calculation ease could likely be found by modeling magnets as volumes of point magnet charges. the force between two charges is mu * q1 * q2 / (4 pi r^2).

I recall it seemed to make the most sense to start with very tiny magnets, but to confirm that it would seem to be good to form a relation between the gravitational force on a magnet and the magnetic force. will a neodymium magnet accelerate more rapidly in a magnetic field if it is small, or large? why?

last time this seemed obvious, which is slightly worrying.