Simply put as the title says. I'm going to handwave that the planet is held together with magic, but I want to know how a magnetic field would work on a toroidal planet- assuming such is even possible. Specifically, I want to know where a 3D compass would point based on where you are.
I see a few possibilities:
Type A: Standard ring magnet shape. I think that 3D compasses would point to an area in the center of the torus, but slightly lifted towards the North side.
Type B: The inner section is North, the outer section is South. I think it would point right at the planet's center of mass.
Type C: One half of the Torus is North, the other is south. Basically just a square bar magnet with a hole in it. It would point towards the inner side of the North side.
Are any of these impossible? (As in, would it likely collapse into no magnetic field, over the course of a few billion years? I dunno much about electromagnetism so I don't know what causes magnets to lose charge.)
Is my understanding of where a compass would point given your position, correct?
If you're in a Type B torus planet, I think if you're on the outer edge, your compass would point somewhere in space, repulsed by the south pole. Is this correct?