# Magnetic Fields: Moving Electrons

• Unicyclist
From the POV of classical E&M, the electric fields act on charges whether they are moving or not. and magnetic fields are generated by and act on moving charges in proportion to their speed. and it turns out, that as long as the speed is less than that of light, the electrostatic repulsion will exceed the electromagnetic attraction.However, from the point of view of someone moving at 1/100th the speed of light, the electric fields would still act on the charges, but the magnetic fields would be "forgotten" because they would be too small to measure.f

#### Unicyclist

Hello, I am new to these forums.

We are studying magnetic fields in my Physics class at the moment and I had a question which my teacher could not quite answer, so I decided to seek some outside help. Anyway, here it is:

Given: Two electrons are moving in a straight line in the same direction. The electrons are abreast of each other and are moving at the same speed.

How I understand it: The electrons are charge carriers, which means that there will be two moving currents and therefore two magnetic fields. The fields are in the same direction so the electrons will be attracted to each other.

Edit: I didn't actually ask a question, did I?
The question is: is my understanding correct?

Have you also remembered to account for the electrostatic repulsion? Which is bigger? What about for current-carrying wires that also have an overall static charge? If you're interested enough, studying this problem leads to special relativity theory.

Have you also remembered to account for the electrostatic repulsion? Which is bigger?
I wasn't sure if it would remain there to act on the electrons or if it would be 'transfered' into magnetic attraction. After all, electric fields act on static charges and these are two moving ones.
What about for current-carrying wires that also have an overall static charge? If you're interested enough, studying this problem leads to special relativity theory.
I was hoping that someone would explain the concept or at least tell me which direction to look in. My teacher already told me it's special relativity, but that's a pretty broad field, I think. Something more specific, maybe?

I wasn't sure if it would remain there to act on the electrons or if it would be 'transfered' into magnetic attraction. After all, electric fields act on static charges and these are two moving ones.

from the POV of classical E&M, the electric fields act on charges whether they are moving or not. and magnetic fields are generated by and act on moving charges in proportion to their speed. and it turns out, that as long as the speed is less than that of light, the electrostatic repulsion will exceed the electromagnetic attraction.

I was hoping that someone would explain the concept or at least tell me which direction to look in. My teacher already told me it's special relativity, but that's a pretty broad field, I think. Something more specific, maybe?

here's the relativistic thought: these two abreast electrons are moving at a constant velocity, right? what if you, the observer, is moving alongside the two electrons watching them? they are moving at all, as far as you observe and since you are all moving at a constant velocity (no acceleration), there is nothing to say that it is you (and the two electrons) who are moving rather than the other stuff you're moving past. it's just as reasonable to say that you (and the two electrons) are stationary and all this other stuff is moving past you. so if the (free) electrons are not moving and they are identically charged, what motion do you expect of them?

Hello, I am new to these forums.

We are studying magnetic fields in my Physics class at the moment and I had a question which my teacher could not quite answer, so I decided to seek some outside help. Anyway, here it is:

Given: Two electrons are moving in a straight line in the same direction. The electrons are abreast of each other and are moving at the same speed.

How I understand it: The electrons are charge carriers, which means that there will be two moving currents and therefore two magnetic fields. The fields are in the same direction so the electrons will be attracted to each other.

Edit: I didn't actually ask a question, did I?
The question is: is my understanding correct?

That is a very difficult question that requires special relativity.
It foiled Gauss and Maxwell. In fact that is why Einstein's first SR paper was entitled "The Electrodynamics of Moving Bodies".
The first step is to write E for one electron in its rest system.
Then, SR must be used with care to find E and B in the system where the electron has velocity v.
In that system, you can calculate the "Lorentz force", F_L, on the second electron.
But you are not through. F_L=dp/dt which must be related to dv/dt using SR for that.

at least tell me which direction to look in. [..] Something more specific, maybe?

Instead of having a couple discreet electrons move in free space, imagine a pair of wires carrying some continuous current. Also give the wires exactly enough excess static charge so that they neither attract or repell (since something so qualitative is unambiguous).

Now, consider this same picture, from the point of view of someone moving at such a velocity that they see the current-electrons move with equal and opposite velocity to the (positively charged ions composing the) wire. Are the forces still equal? If you uncover a paradox, you'll see you can fix it by introducing a certain amount of "length-contraction"..

I was hoping that someone would explain the concept or at least tell me which direction to look in. My teacher already told me it's special relativity, but that's a pretty broad field, I think. Something more specific, maybe?
You haven't mentioned what level you are on. The answer requires relatliviy.
If Maxwell couldn't do it without SR, neither can we. The only adequate treatment of this that I know of is in graduate EM texts.

Actually Purcell gives a nice treatment of the relativistic fields and forces of uniformly moving charges in his freshman text "Electricity and Magnetism", (vol. 2 of the Berkeley Physics Course).

You haven't mentioned what level you are on. The answer requires relatliviy.
If Maxwell couldn't do it without SR, neither can we. The only adequate treatment of this that I know of is in graduate EM texts.

I'm doing my A-level. I guess I'll have to wait till I go to university till it can be explained to me properly. Oh well. I got the general idea from the posts above, it's enough for now. Thanks to everyone.

Also, I feel sort of proud for asking a question that stumped Maxwell.

I'm not sure what "A" level is, being in the US where we use a different system.

You'll definitely need special relativity to answer this sort of question.

There is some treatment of the topic online, though. Start at http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_1.pdf

and work you way up to http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf

which gets into the electromagnetic aspects. It will probably be too terse of a treatment unless you've already read some introductory books on special relativity, though.

For textbooks, you can try Griffiths
https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20, the other recommendations are also good.

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I looked at the Field pdfs. They don't get to B or how E and B would affect the motion in SR. I would not recommend trying to learn SR from these pdfs.
I assume they are meant to supplement Field's classroom discussion.
Griffith's discussion of this is somewhat convoluted, because he tries to avoid tensors in the derivation. Using tensors would make make it all simpler. Also Griffith's does not address the question of how the E and B fields affect motion in SR.