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I'm trying to estimate the magnetic force which develops on a truss-like ferromagnetic structure (I want to estimate the motion of the object) in a uniform magnetic field, and I came to realize that I have a fundamental gap in my knowledge.

My question is: how do I calculate the magnetic force in a uniform magnetic field with magnitude $B$, related to a rod-like object with length $L$, diameter $d$, and mass $m$?

From what I could fathom so far, the force should be independent of the mass. It is mainly depended on the intensity of the field.

An initial guess is that the force should be independent of the mass. However, that cannot hold because then what happens if I take two masses and glue them together?

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  • $\begingroup$ What makes you think that gluing two masses together would be different than merely placing them side-by-side? $\endgroup$ – Wasabi Sep 29 '20 at 13:45
  • $\begingroup$ nothing really. Just pointing out, that if you put one rod of mass m if you get a force of 1 N, and you get a second mass with another 1N, then that would sum up to 2 N. However, if Force is independent then mass shouldn't matter. $\endgroup$ – NMech Sep 29 '20 at 13:54
  • $\begingroup$ Why do you expect gravity to have no role in your system dynamics? $\endgroup$ – morbo Sep 30 '20 at 7:02
  • $\begingroup$ @morbo Gravity will play a role. However, I am wondering if the mass of the iron will also play a role. More iron to my mind means that there is more material that can become magnetized. $\endgroup$ – NMech Sep 30 '20 at 7:05
  • $\begingroup$ Don‘t forget hysteresis, magnetic saturation...and the affect gravity will have, as you increase your mass...you could easily do a balance of your forces and see which one dominates $\endgroup$ – morbo Sep 30 '20 at 7:12

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