Magnetomotive forces acting on assembly

Apologies if this is the wrong place to pose this question, or if it is poorly formulated, I would appreciate any help, even if that is pointing me to a place where I can learn more about solving problems like this.

I’m trying to work out what is going on in the following assembly of magnets (neodymium) and magnetic materials (probably steel) / non magnetic materials (probably plastic).

The assembly contains three rows, which are free to move horizontally, but constrained on the other axes. And, each row can move independently of the others.

What I would like to do is make a computer model of this system, and just play around with the parameters to get a feel for what happens with different numbers of magnets, different arrangements of the steel pieces, etc.

So my question is how would I compute the net magneto motive force acting on each component in this assembly?