Rigorous definition of magnetic poles?

[greypilgrim]

Hi.

Since there haven't been observed magnetic monopoles so far, what exactly do we mean when we talk about the north/south pole of a magnet? Is it something like "north is where the field lines exit a solid body" and "south is where they enter" or is there a more rigorous definition?

 

[mfb]

You can find the main axis (given by the dipole moment), but assigning points like "exactly here is the pole" doesn't make sense. Typically one half of the magnet is called south pole and the other half is called north pole, but that doesn't work for more complex magnet shapes where the definitions get a bit arbitrary.

 

[Vanadium 50]

There is a rigorous definition, but not at the B level. It involves vector calculus, and the idea is that if you have a volume where you have more flux lines going in than out it contains a pole. Magnetic fields do not do this, so the best you can do is point to some non-enclosed region and say "this region is pole-like".