I know there's already a topic similar to this, but I'll try to give it a better start.
I've just finished studying magnetism in physics. I don't know if anyone else has studied it, but it seems very strongly dependant on having three dimensions. Many of the laws of electromagnetism require three perpendicular vectors i.e. magnetic field, current and the force acting on the wire.
I found it interesting that these were actually three interchangeable aspects of the same force, and also that they were always perpendicular to each other, because we have three dimensions.
How do you think magnetism would work in more or less than three dimensions? I suspect that the electromagnetic force actually works in n different ways, where n is the number of dimensions. Therefore in 2D, magnetism wouldn't exist at all, only electricity and the "pushing" kind of force. In 4D, perhaps there would be two kinds of magnetism, or perhaps a new kind of electromagnetism altogether.
Alternatively, magnetic fields might just work differently in other dimensions. Maybe they oscillate around a wire in 2D and have some kind of spherindrical motion (like cylindrical, but with a spherinder) in 4D. Which is the more likely scenario?