Let's consider a single charged elementary particle (i.e. NO internal structure, such as the electron) in its rest frame. Does it produce a magnetic field because of its spin? Would a neutral elementary particle with non-zero spin at rest produce any magnetic field? If yes, what expression should the magnetic field have? Does it make any difference if the particle is a fermion or boson?
[Physics] Do elementary particles at rest produce magnetic fields
electromagnetismmagnetic fieldsquantum-spin
Related Solutions
Still is there electric field around it?
Yes. The electron is moving (in our reference frame), so now there is a magnetic field (in our reference frame), but nothing happens to the electric field.
i. If it has electric field around it, why is it that when electrons are moving in a conductor (i.e.. current if flowing in a conductor) there is no electric field outside the conductor?
The electrons in the conductor produce an electric field outside the conductor; however, realistically, there will be just as many protons in the conductor as electrons, and hence the net electric field outside the conductor is zero.
ii. Now, when a current is flowing in a conductor (I'm not sure what happens if the motion is not inside conductor) it produces magnetic field around it. I'm lost. What happened to the electric field? Is it still there? Are there both electric field & magnetic field? Why don't we discuss about it?
The electric field is still there (in some sense), but its zero, because the electrons and protons in the conductor cancel each other out, so we don't care about it. (Actually, I believe that if you take into account relatavistic effects, which is probably silly not to do in the context of electrodynamics, there will be a nonzero electric field). That being said, if for some reason there were stream of moving electrons with no protons, then we would observe both a (nonzero) magnetic and electric field.
- Hypothetically, If the electron is moving with speed more than that of light. What happens now?
Special relativity says this can't happen :). In any case, if we play dumb for a moment, the only thing that would change is the current, and hence the strength of the magnetic field.
How do we know that there exists such a particle as the muon?
From observing its decay into an electron plus two other neutral particles, which are an antineutrino electron and a neutrino muon.
In this last sentence there are three conservation laws:
1) conservation of charge ensures that the muon has the same charge as the electron
2) lepton number conservation ensures that the number of particles with muon leptonic number and the number of particles with electron leptonic number are conserved.
These are observations, the accumulation of which together with a large number of other observations allows us to build up the standard model 0f particle physics. The Standard Model encapsulates our observations/data.
The short answer to the question is: because that is what has been observed.
Best Answer
Both electrons and neutrons at rest produce magnetic fields because they have non-zero magnetic moments.
The electron moment is $$ {\boldsymbol \mu}= \frac{eg}{2m} {\bf S} $$ where the spin ${\bf S}$ has magnitude $|{\bf S}|=\hbar/2$ and $g\approx 2$. A point dipole with magnetic moment ${\boldsymbol \mu}$ produces a field with spherical polar components $$ B_r= \frac{\mu_0}{2\pi} |{\boldsymbol \mu}|\frac{\cos\theta}{r^3}\\ B_\theta = \frac{\mu_0}{2\pi} |{\boldsymbol \mu}|\frac{\sin\theta}{r^3} $$ where the moment is aligned along the $z$ axis.