I am using a Magnet like this in an assembly and I am trying to calculate the torque in point P2 (see picture below) resulting from the attraction force F between my magnet and the steel part.

As I assume that the magnetic force is a volumetric one, I am not sure which distance to point P2 to take for my torque calculation.

In the case of an equidistant gap (no tilting) between the rotational symmetric Aluminium part which is carrying the magnet and the Steel part, I think the resulting Force can be seen as it is applied in the center of the magnet which is in a distance of L1 to P2?

Force resulting from magnet without tilting

Therefore, in this case the resulting torque around P2 would be: M=F*L1. Please correct me if I'm wrong.

But in the case of tilting I am not sure which distance (L2 or LP) to consider for torque calculation. As P1 is the only contact point between the two parts it might be the point where the load on the steel plate is applied?

This would lead to M_tilt = F*LP. Force resulting from magnet with tilting

Thanks for your help!

  • 1
    $\begingroup$ You'd need a pretty special magnet to apply force anywhere close to this uniformly. It will be distributed with location of the poles of the magnet, and in case of your tilt, it varies with inverse 7th power of distance from the steel. $\endgroup$
    – SF.
    May 6, 2021 at 10:22
  • $\begingroup$ @SF I would be very interested if you could point to some introductory reference material I can read so that I can derive the 7th power. Magnetic forces are still a bit of a black box for me. I'm even tempted to put it as a new question! $\endgroup$
    – NMech
    May 6, 2021 at 12:16
  • 2
    $\begingroup$ @NMech Ask around on Physics.SE I found someone tell me that there and it was enough to completely extinguish my desire to dig deeper - it's not an easy subject, Normal magnet-magnet interactions tend to vary with square of distance and are a "regular difficulty" subject to study, but inert non-magnetized iron/steel becomes a magnet the stronger the closer to a permanent magnet it gets, that in turn increases the field strength which makes it magnetized even stronger, and the exponent of the distance really explodes, and the mathematics of this becomes really difficult. $\endgroup$
    – SF.
    May 6, 2021 at 12:46
  • 2
    $\begingroup$ As for practical, real-life applications, probably an experimental / measure approach would be most practical. The magnet's attraction strength will vary with steel composition, thickness (irrespective of mass), magnetic permeability of possible coating and the aluminum casing, and other factors you may not even be aware of, never mind be able to include in calculation. $\endgroup$
    – SF.
    May 6, 2021 at 12:50
  • $\begingroup$ wow 1/x^7 , didn't know! Besides that the hysteresis and saturation effects are very pronounced. If OP only needs the location known, and magnitude can vary, then one could potentially concentrate the magnetic field lines with another piece of ferrous metal. 3D structures also exist that shape the field into a relatively uniform one over a selected space - these work well enough that magnetically actuated proportional valves can be reproducible to under 5% (after the hysteresis is eliminated with an AC signal). However this is electromagnet acting on thin steel. $\endgroup$
    – Pete W
    May 6, 2021 at 16:04


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