Force generated by a solenoid on a moving steel ball bearing

[thephysicsgod]

Hi, I want to find an equation for the force generated by a solenoid on a moving steel ball bearing given current, number of loops, area of the solenoid for a lab project. I've tried looking through many sources, but was unable to find anything. I also tried looking at this previous discussion https://www.physicsforums.com/threads/equation-for-f-using-flux-desnity-in-solenoid.328605/ but this is for a steel ball bearing that isn't moving. Any help would be greatly appreciated.

 

[mfb]

The motion will induce eddy currents, those are independent of the ferromagnetic reaction of the steel balls.
In general the interaction between magnets and magnetizable objects is very difficult to calculate.