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Due to electron "spin", a small magnetic field is produced. Maxwell's equations imply that magnetic fields are due to changes in electric fields. Is the magnetic field produced then because the electric field is "spinning" with the "spinning" electron, in the quantum sense of "spinning" and this change in electric field is generating the magnetic field?

Can one generalize to say that the magnetic field thus would spin when a magnet is spun?

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Related: physics.stackexchange.com/q/41678/2451 –  Qmechanic Jan 31 '13 at 14:48
    
Maxwell equations state that a varying electric field produces a magnetic field, but not necessarily every magnetic field is produced by a varying electric field. The spin of a particle produces (for not straightforward reasons) a magnetic dipole, which produces a magnetic field independent on charge motions. –  Bzazz Jan 31 '13 at 16:01
    
Thanks. Do you know how to calculate the magnetic field produced then without Maxwell's equations. –  Mew Jan 31 '13 at 23:14
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If by "spin", you mean rotate around its axis, like the earth does every 24h, then it is incorrect that the electric field of a point particle spins. A point particle doesn't have dimensions so it doesn't have an axis to rotate around and thus no magnetic field is produced.

The property of "spin" of elementary particles is not caused because of their rotation.

Now, the magnetic fields are different because there are no magnetic monopoles, so a magnetic field does rotate when the magnet is spun.

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How do you explain the magnetic field produced by "electron spin" if not by a change in electric field? –  Mew Jan 31 '13 at 14:59
    
Spin is an intrinsic property, as far as we know, just as it's mass. It is associated with an angular momentum, but it is quantized, and the group of symmetries is not the same as the group of symmetries of spinning macroscopic objects. The latter is SO(3) and the former SU(2). The difference,roughly, is that in the second one, after a rotation of 360 degrees, you get to the initial state with a minus sign. –  Barefeg Jan 31 '13 at 15:06
    
I understand that. I am wondering how the magnetic field results from this "spin". –  Mew Jan 31 '13 at 15:06
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You cannot obtain the magnetic field as you would in the classical case. Because charge zero particle also have spin so you cannot suppose that the charge is distributed in a tiny sphere and work out the magnetic field. –  Barefeg Jan 31 '13 at 15:46
    
How do you calculate the magnetic field then? I've only come accross the classical calculation, so please explain the non classical calculation. –  Mew Jan 31 '13 at 23:15
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