Permanent Magnetic Dipole in an electromagnetic field

[Aviax98]

I've been trying really hard to calculate the forces between a permanent magnet that is within an electromagnetic field.
I have tried every formula under the sun, but it seems I am just not using the right ones, as my results always end up nonsensical.

To be clear, I am trying to understand the math behind a project like this one:
https://kevinlynagh.com/pcb-stepper/
However, the math here just doesn't look right. The OP seems to just drop off terms from the formulas and make strange jumps in their logic.

Would anyone be able to point me in the right direction as to what formulas I would need to figure out the math behind a system like this? I don't even need it to be perfectly accurate, just an approximation would suffice.
Thanks all!

 

[Baluncore]

Welcome to PF.

It seems you are getting into linear induction or stepper motors.

First, you need to understand the history of linear motors and why they are difficult to design. There are not only horizontal forces along the plane, there are also vertical forces, that can stick the carriage to the track, or throw it up in the air.
A History of Linear Electric Motors. Eric R. Laithwaite. 1987.

Second, you need to understand the materials, do some field mapping, and then some calculations. Take a look at;
Linear Synchronous Motors: Transportation and Automation Systems. 2'nd Edn, 2012.
Jacek Gieras, Zbigniew J. Piech, and Bronislaw Tomczuk.

 

[Aviax98]

Hi Thanks for your reply and your suggestions!
I will have a read of those and see how I go.