# Magnetism as a relativistic effect

So my physics teacher has been trying to explain magnetic forces in terms of electric forces and relativity but I'm still confused. If there is a wire carrying a current and I'm an electron traveling next to the wire at the same speed the electrons in the wire are traveling, the electrons in the wire are motionless in my reference frame but I see the positive ions as whizzing past me. due to length contraction the separation of the positive ions appears smaller than the "motionless" electrons and so I see a net positive charge and I'm attracted to the wire.I understand this.However, If I am an electron sitting still next to the wire the positive ions are motionless in my reference frame and the electrons are whizzing by me and so (due to length contraction) I should see the electrons as more "bunched up" and I would be repulsed by what appears to be a net negative charge?Likewise, If I'm an electron and there is a stream of just positive ions flowing past me as I am motionless shouldn't I be attracted to them regardless of whether or not i see them as more dense then they are. but apparently that's not what happens.Moving charges don't affect motionless charges so whats going on?

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The idea of a moving charge feeling a force towards a wire carrying current being caused just by the lorentz contraction of the charges in the wire is a simplified analogy, and like all analogies it breaks down if taken too far. To fully realize what's happening, you have to take into account time dilation and the shrinking and stretching of the electric field.

Bill_K
A lengthy discussion of the magnetism produced by a current-carrying wire from this point of view can be found in "Special Relativity" by A.P. French starting at p.256.

Dale
Mentor
However, If I am an electron sitting still next to the wire the positive ions are motionless in my reference frame and the electrons are whizzing by me and so (due to length contraction) I should see the electrons as more "bunched up" and I would be repulsed by what appears to be a net negative charge?
No, the wire is uncharged in the wire's frame. That is part of the initial set up of the problem, it is uncharged and carries a current in that frame. You use that given fact plus length contraction to explain the forces in other frames, but you cannot contradict any of the given facts.

Hi cdot:

Try this short read for perspective on 'frames'...what is at rest and what is 'moving':

http://en.wikipedia.org/wiki/Relativistic_electromagnetism#The_origin_of_magnetic_forces

Iassume this is the setup you are using.....Maybe we can learn something together... since I have never studied this explanation.....

If there is a wire carrying a current and I'm an electron traveling next to the wire at the same speed the electrons in the wire are traveling, the electrons in the wire are motionless in my reference frame but I see the positive ions as whizzing past me. due to length contraction the separation of the positive ions appears smaller than the "motionless" electrons and so I see a net positive charge and I'm attracted to the wire. I understand this.
ok, I agree you understand and I get the same result...this seems to match figure 5 in wikipedia with charge sign reversed....

However, If I am an electron sitting still next to the wire the positive ions are motionless in my reference frame and the electrons are whizzing by me and so (due to length contraction) I should see the electrons as more "bunched up" and I would be repulsed by what appears to be a net negative charge?
Now you have assumed the frame a test charge stationary wrt the wire, not any of the charge flow.....so I think positive charges flow one way, negative another, relative to you, with equal speed; but the total charge remains fixed and neutral.....same number of positive and negative carriers....in this 'simple' model there would appear to be no force....

This does NOT fulfill the alternative scenario represented in Fig 6 of Wikipedia....stationary with respect to one of the charge flows [not stationary with respect to the wire]. So of course you get a different result with your different scenario.

Likewise, If I'm an electron and there is a stream of just positive ions flowing past me as I am motionless shouldn't I be attracted to them regardless of whether or not i see them as more dense then they are. but apparently that's not what happens.
Then you must be moving someway wrt the positive charges, maybe faster than them for example in the same direction, maybe with the negative charges....so what effects you measure would not be obvious to me.

Moving charges don't affect motionless charges so whats going on?
I'm unsure just what you had in mind with this comment....For one electromagnetic field IS affected by relative motion. instead, look at it this way: if you first are the 'motionless' test particle and see the other charge moving relative to you, then reverse positions...now you will see the former particle particle moving with equal but opposite velocity....just like two cars observe each other with the same relativte speed. (If I pass you going 20 mph faster, you see me going past you by the same amount.)

Hope I got that right; hope it helps....If I did make a mistake, someone will be sure to provide the requisite ridicule !!! I'll try to come later to double check and edit this ....[edit: post #5 appeared while I composed...will have to read that, too.]