Equations for finding magnetic force between magnet and solenoid

Hi everyone.

I was doing an experiment on the effects of varying the distance between the solenoid and magnet, the voltage across the solenoid, and temperature of the iron core inside the solenoid on the magnetic field produced and the magnetic repulsion between the solenoid and magnet.

The magnet was placed on a scale with blu-tack and the solenoid with the iron core was placed above with a retort stand. Those variables were then changed one at a time.

My question is, how do I find the theoretical force of repulsion between the magnet and solenoid? I already have the readings (tared). I have found some equations, however I lack information on the iron core and do not know how much it affects the magnet field. What is its permeability? I read that it varies.

I have found this formula for finding the force:

[itex]F=\frac{\mu_{0}m_{1}m_{2}}{4\pi r^2}[/itex]

And also for finding the magnetic pole strength:

[itex]m=\frac{NIA}{L} [/itex]

But since I have an iron core, wouldn’t that affect magnet pole strength? It only has number of turns, current, area and length in the equation.

Also how would I find the magnetic pole strength of the permanent bar magnet that I used?

Thank you.


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