Presumably the electron's magnetic field must project some distance into space in order for it to react with an externally-applied field (Electron Spin Resonance etc.) ... so I would have expected some of the field to go out to infinity, just like any other magnet, although this field diminishes by an inverse cube law and so gets very small very quickly.You're confusing the extent of the field with the direction of the field lines. For a magnetic dipole field (such as that of a bar magnet) there will be field lines arbitrarily far away (i.e. the field exists arbitrarily far away, though its strength goes down). However, you can't follow any given field line from the magnet to infinity. As long as you stay on the same field line, you will end up going back to the magnet.
What about the field line that continues the straight line between the two poles? Imagining a universe with no other magnetic fields to confuse the issue, of course.
Then I thought about this ... the inverse cube law calculation contains the distance between the poles as a parameter. If the electron is a point particle then the distance between then poles is zero, which means no external magnetic field ... so how does it work? I suspect quantum weirdness again.By distance between the poles, do you mean the distance between the charges making up the electric dipole? I'm trying to understand what your problem is here.
No I mean the distance between the poles of a bar magnet (or equivalent). If you calculate the field at a distance from a magnet which is significantly greater than the distance between the poles then it tends towards being inversely proportional to the cube of the distance and linearly proportional to the distance between the poles (tending towards proportional to 2d/x3
, if I've done the calculation right, where d is the distance between the poles and x is the distance away from the centre). Obviously, if d=0 (how could it be anything else for a point particle) then it appears the magnetic field has to be zero everywhere. To look at it more simply, if both poles are in the same place then at every point in space the fields from the two poles cancel out.
But of course this is a classical physics argument. In classical physics a point particle can't have spin and we know an electron has quantum spin, so presumably it has some sort of quantum magnetic field as well.
Quantum weirdness gives me a headache ...