Here is my assumption: The opposing magnetic flux along the sides of these bar magnets lends repulsive force, weak but it is there.
In case that initial assumption is correct, that would scale up to an iron rod inside a solenoid, or, equivalent, a bar magnet inside a hollow cylinder magnet, repelling along the sides (while attracting at the poles. )
That in turn scales up to a sphere magnet inside a hollow sphere magnet, repelling along the sides while attracting at the poles.
And finally, to an electric coil inside a hollow sphere magnet, the two bodies locked at rotational axis by electromagnetic attraction, with repulsion along equator and sides.
