To any nonmagnet, the whole sphere is a magnet. To another spherical magnet thou

Question

To any nonmagnet, the whole sphere is a magnet. To another spherical magnet though, there is a rough area on the surface where it is strongly repelled.

Given a spherical magnet, how should the poles be found?

My crude attempts were as follows

Grip one sphere in a forceps
Bring another sphere close to the forceps
Rotate/roll the spheres until the most repulsion is sensed
Mark the facing surface of the sphere in the forceps using a permanent marker

The trouble with the above approach is that I rely upon tactile memory to determine maximum repulsion.

Is there a better, inexpensive way to do this?

Explanation / Answer

If the magnet can support its own weight, I'd stick it on the underside of a piece of well leveled, (ferromagnetic but not magnetized!) sheet metal. It should hang from one pole or the other, as the center of mass of the magnet should end up vertically in line with the strongest part of the pole.

assume the sphere is in contact at some point other than where the flux density is max (i.e., the pole). The distribution of the field around that contact point will be asymmetric. In particular, the region of maximal flux density should attract the plate more than other points at the same angle away from the contact point. Most of this force would be upward, but there would be a slight tangential component (going as sine of the angle of contact-center-pole) that should torque the sphere so as to roll until the pole produces no such torque, as happens when the poll IS the point of contact

the torque being proportional to the sine of the angle is problematic, though, in that it wouldn't take much to influence where the equilibrium point lands. the plate should be smooth, as should the magnet, to reduce any kind of friction that would prevent rolling. Any kind of field in the plate would hugely skew the result.

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