Moving charges and magnetic fields

  • #1

I was just thinking about the simple concept that a moving electron produces a magnetic field at right angles to its travel... Now here's my question. Since we live in a relativistic universe, what is the charge moving with respect to in order to create the field? If we say the observer, then one is forced to conclude that the electron must always have a magnetic field around it since it is always going to be moving with respect to something... Where am I going wrong here?

- Jason O

Answers and Replies

  • #2
Congratulations! You are thinking subtle and deep thoughts. The way to detect the presence of a magnetic field is to observe its force on a current, that is, on at least one moving test charge. Accordingly, you have a system of two (at a minimum) charges. If both move at the same speed as seen in the lab frame, then in their rest frames they see each other at rest and feel an electrostatic attraction or repulsion. In the lab frame they appear to be responding to each other's magnetic field.

The major, deep conclusion is that magnetism is just a relativistic manifestation of the Coulomb interaction. The precise relation is through the electromagnetic tensor, which you can look up in an advanced E&M book or online at, eg., Wikipedia.
  • #3
consider two cases, both with two electrons.

the first case is where the two electrons whiz by an observer with constant and identical velocities (both direction and speed, so they are not moving relative to each other). the observer concludes one electron is generating a magnetic field and the other electron is moving through the magnetic field and is therefore affected by it and the observer see that. there is, of course, the electrostatic interaction besides the magnetic interaction.

the other case is identical except now the observer is moving alongside the two moving electrons at their velocity. this is a constant velocity, an inertial frame of reference, so it is just as legitimate as any other inertial reference frame, including the one of the "stationary" observer in the first case above. but now what does the observer see? any magnetic field getting generated? from this observer's POV is the other electron moving through a magnetic field, even if one were generated? there remains the electrostatic interaction, though, in this reference frame even if there is no magnetic interaction.

both POVs are inertial and equally valid. how do you resolve the differences of observed behavior between the two?

you can do this thought experiment even better with two identical, infinite, and parallel lines of charge.
  • #4

Thanks for the insights here. Ok, here's another question to, hopefully, clarify my understanding here. Let's say, for instance that there is a piece of wire with an AC current flowing through it, and next to this piece of wire we have a negatively charged plate. If we observe the electrons in the wire from the charged plate's prospective, one would expect to see a changing magnetic field exerting a force on the particles in the plate.

Now if one is in the wire moving with the flow of electrons in the wire, the particles on the plate would appear to be moving back and forth so this means that the charges on the plate would appear to be producing a magnetic field that is acting on the charges in the wire right?

- Jason O

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