The basic set up for a homopolar generator has a stationary magnet and a rotating conducting plate with contacts at the center and rim of the plate. I would think that even if magnet were spinning along the same axis, the magnetic field would not materially change and so the resulting current would be the same. What if, instead of a separate plate, the magnet were spinning and had contacts attached in a similar way? Would there still be a current induced? To clarify, the poles of the magnet are aligned with the axis of rotation. I don't really have an understanding of how conductivity would change when an object is magnetized. This may be the real issue.