After reading your answers (thanks), and rethinking, I now believe that:
- if the magnet core was already near saturation, then inserting the iron plug would significantly decrease the leakage flux in that area (because the flux within the magnet cannot increase much and almost all of the flux will be channeled through the iron plug)
- if the magnet core is far from saturation and the flux strength was regulated only by the air gap, then inserting the iron plug would decrease the leakage flux only slightly (because the flux within magnet will greatly increase)
- in any case, the leakage flux will not increase.
Unfortunately, it does not answer me what happens with the force:
- if the force only depends on the leakage flux, then it will decrease
- but if the force depends also on the flux within the magnet (because two flux fields interacts) then the force can also increase under some circumstances - that is, in the case when the flux internal to magnet increases a lot after inserting the plug.
What do you think?
(Note: whenever I read about the force excreted on a current-carrying wire, the text always talk about flux density the wire is immersed into. But from the beginning I am not sure what the word 'immersed' actually means - does it include nearby magnetic fields that are not really 'touching' the wire but are within the reach of the wire-generated magnetic field?)