# What would happen if a rotatable ferromagnetic rod were placed beside a magnet?

If one were to place a rotatable shaft (green circle), made of plastic with ferromagnetic material (grey circles inside green circle), right beside an electromagnet, what would happen? I am trying to exclude the case where the shaft has magnets on it as a thought experiment.

For instance if the green circle were the rotatable shaft in this picture, would the shaft rotate due to the magnetic force?

Alternatively, is there an orientation that will cause the shaft to rotate? This would seem to be a perpetual motion machine (which doesn't make sense).

• Could you expand a bit on why you think the shaft might rotate? Dec 20, 2018 at 15:47
• The arrow lines doesn't work that way. They only show how the magnetic field is shaped. And yeah, never kid yourself to believe that perpetual motion machines exists. It's only wasting time for you, and for us. Dec 20, 2018 at 16:03
• I'm more interested in the thought process leading to the contradiction that this would rotate. Dec 20, 2018 at 16:12
• @JordanMcBain If you need to be contradicted... then.. have faith. Where we don't need to prove anything. Dec 20, 2018 at 16:29
• The closest magnetic part of the rod is attracted with the strongest force. So no other force (from the other attractions) will overcome it. You can write down some (not-that-complex) math proving it. Dec 20, 2018 at 17:58

Assuming that the shaft is constrained only to rotate, the shaft would rotate by a certain angle to settle at the point of stable equilibrium. This point of stable equilibrium would correspond to the one where the flux lines are offered the path of least reluctance. This is similar to what happens in a switched reluctance motor. Of course, there won't be perpetual motion since there is going to be only a single position of equilibrium (depending on the orientation, shape, and sizes of the ferromagnetic material).

From an engineering point of view, it may be noted that the reluctance offered by the plastic part is more or less the same as that offered by an air gap of the same length (same permittivity). The speed and the associated oscillation rate at which the rod would settle at equilibrium would depend upon the above factors, the strength of the magnet and the friction coefficient. The system can be modeled mathematically in s-domain to obtain the dynamics. However, as for the steady state, the rod would settle at an equilibrium position and move no further.

If the shaft can not move an any direction except to rotate the magnet will have little effect. If the shaft were to rotate due to some other force, there would be a braking force due to eddy currents induced in the shaft. The resistance of the shaft would tend to minimize that effect. The effect would be maximized if the shaft would be copper plated.