electromagnetism - Orientation of sphere magnet inside sphere magnet

A sphere magnet inside a sphere magnet, both hollow, which of the two orientations will it prefer?

Answer

Since polarisation is vertical, inside the outer sphere, the «blue pole» is below the top hemisphere (i.e. on the inside of it). Since the opposite polarity will get attracted to it, this means the inner sphere red pole will also face upward (i.e. left picture), given the inner sphere has a way to rotate freely inside the other one.

I should add that the inner sphere is like an inner extension of the outer one, i.e. they should both have the same pole orientation. You could take a full sphere and remove outer layers and will still find the same polarity, assuming the entire sphere was magnetized at once by the same field.