 # Do all moving charges create a magnetic field?

From what I sort of understand, a moving charge produces a magnetic field. So when electrons move through a wire, that motion produces a magnetic field. But is that true for all charges? Would moving protons, anti-electrons and anti-protons all produce magnetic fields? If so, would they be different than the normal magnetic field produced by electrons?

Also, is the strength of the magnetic field proportional to the relative difference in speed? For example, if 3 electrons move past me at different speeds–one moving very fast, one moving slower, and one moving very slow–would I feel different amounts of magnetic force from each one?

Yes to all of your questions. The magnetic field produced by a moving charge depends only on the value of the charge and its motion. Though I suppose that the proton or anti-electron would be a field in the opposite direction (though same strength) from that produced by an electron or anti-proton.

I’ve a hunch that there’s going to be a follow-up question, and that the answer will involve relativity, but I’ll wait until that’s asked.

I would like to add that electrons all move at the same speed in the same medium, the speed of light. A vacuum is fastest, air a little slower and metals even slower all pretty close though. There are exceptions but that is the world of physics labs and the like

And I would like to add that what Capt Kirk just said is completely wrong. Electrons, like any particle with mass, never move through space at the speed of light.

Not a single thing you’ve said here is correct.

No, electrons are fermions and therefore have mass and move at speeds less than c. Photons do move at c in absence of an interfering, but have no charge and do not, by themselves, generate magnetic field.

Stranger

I think Scotty needs to explain it just one more time…

To my knowledge, there is no reason a fermion cannot be massless, and as far as I know, the jury is still out on whether or not the electron neutrino and its antiparticle have a nonzero mass.

Yeah, there is no reason a fermion must have mass.

Thanks for the info. A couple of followup questions.

Could the magnetic force between two electrons be strong enough to pull them together if they were moving fast enough relative to each other? Say you had two electron guns pointed at each other firing very fast electrons. When those electrons pass near each other, what happens? Would they curve nearer from the magnetic attraction or diverge from the electrical repulsion?

And a random question… Is charge constant or is it related to motion like magnetic force? Will I measure an electron’s charge the same regardless of it’s relative motion to me?

Not only do electrons not go the speed of light, they often go pretty damn slow. I recall an old physics homework problem where we calculated the speed of electrons moving through a wire. IIRC it was on the order of a few feet per second.

Remember that the electrical repulsion will alone cause the electrons to deflect, regardless of any magnetic field that is produced. For two parallel-moving electrons, there is no extra deflection or attraction from if they were stationary: the magnetic field exactly compensates for relativistic length-contraction of the electric field. We know this because the physics must be the same in the frame of reference in which the two charges are at rest. Note that this is different from the case of a current in a wire, where the electrons’ motion is relative to oppositely charged protons in the wire. For charges shot at each-other, there is no frame of reference in which both charges are at rest, and so there is a slight change in deflection due to the magnetic field, or alternatively the relativistic length-contraction of the electric field, depending on which frame of reference you choose to study the problem in.

Charge is constant.

To be fair, that calculation is the *net *flow of electrons through the wire. The electrons themselves were probably moving much faster (although still not light speed) just in a drunkard’s walk so convoluted that they drift in the direction they are going only at a walking pace.

A related phenomenon is this: what is the force between two electrons as measured in a frame where they are moving along parallel tracks at a speed v? If you figure out how much electric and magnetic field each one creates, you find that the magnetic force on each electron generally opposes the electric force on it, and the magnitude of the magnetic force increases relative to the electric force as v increases. In fact, the electrons would experience no net force in the limit as v approaches c.

Not quite the same configuration as you’re describing, but consider this:

about twenty years ago my brother was pursing a Ph.D. project that involved high speed imaging using a camera with a 10-million FPS frame rate. The camera achieved this frame rate by first converting the incoming image into an electron beam, which it could then rapidly steer to different regions of a phosphor plate. Bright areas of the image corresponded with high electron flux in the electron beam; because the electrons were attracted to each other (owing to the elecromagnetic force they generated via their motion), bright regions of the image appeared “pinched” - that is, if you had an image with two white quadrants and two black quadrants, the black quadrants appeared to bow into the white quadrants. My brother was able to model (and correct for) the distortion based on the equations describing electromagnetic attraction.

Charge is constant. An electron has a charge of −1.602176565×10[sup]−19 [/sup] Coulombs.

Yeah, thats true. Now you’ve got me wondering how fast they move at a smaller scale. Of course at a small enough scale talk of them “moving” probably doesn’t make sense.

That can’t be the whole story. There would be no electromagnetic attraction between the electrons (like signs repel, and the relativistic correction for parallel beams is zero).

oops I stand corrected thanks

Are you talking about two electrons moving at the same speed in the same direction along parallel tracks? If so, couldn’t you just do the force calculation in the reference frame where they are both at rest (where there are only electrostatic effects) and show that the total force is constant at all speeds?