Magnetic Force between Solenoid and Bar Magnet

Hi, I recently conducted an experiment for school where I investigated the relationship between the current flowing through a Solenoid and the resultant magnetic force of repulsion/attraction between it and a bar magnet positioned at a distance vertically below the horizontally placed solenoid.

The experiment was conducted successfully, although I now would like to compare my experimental results to theory; Problem is, I can't seem to find a formula describing the Force between a solenoid and a Bar Magnet.

I thought something similar to coulombs law, but what I found looked sketchy, and the units did not add up.

Any clue? Thanks.