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Concerning two identical wires carrying the same current (same direction, speed and magnitude), they will be attracted because of the Ampere force. But when I was in the frame moving with the same speed as the electron in the current, why will there be the same force between each wire (supposing that the electrons are moving at a speed far less than $c/10$).

Also, when two bundles of electrons are moving in the vacuum at the same speed, will they be attracted because of the Ampere force? Will they be dis-attracted because of the Coulomb force?

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3 Answers

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If you're in the frame where the electrons are standing still, the rest of the wires (which have an equal positive charge, since the total is neutral) are moving in the opposite direction, and provide the Ampere force.

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yeah i know, but what about the second question, the electrons are moving in the vacuum –  Golbez Nov 26 '12 at 13:51
    
The Coulomb force is much more powerful than the Ampere force, so when you add the two forces, the charges will repel. You can see this by considering the reference frame where the charges are not moving. –  Peter Shor Nov 26 '12 at 14:16
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Now, current constitutes of a regular motion of electrons no matter how slow, they are moving all the time, like a traffic, only a continuous line of cars will actually constitute a traffic a single car won't . In the first case only due to the presence of magnetic field the wires are actually attracted to each other. Current can produce magnetic field. In the next situation the two electrons moving in vacuum are alone , therefore there is no current and hence no magnetic field, so the only force would be the Coulombic repulsion force . It is kinda tempting to think Of lorentz force

F = q(v x B) here but since there is no B there is no lorentz force.

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yeah right thanks –  nashmaniac Nov 27 '12 at 13:17
    
Also, your statement about two electrons moving in vacuum not producing a magnetic field is wrong. If it were right, you would have the problem: do two moving electrons in a row constitute a current? How about 100? Or $10^{23}$? –  Peter Shor Nov 30 '12 at 20:09
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Why would the force be different? Since the two wires are identical, what observed in the frame of an electron of one wire would be equally observed in the frame of an electron in the other wire. For the second question, I suppose both forces have to be taken into consideration. You can get the force by the Lorentz force $q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$.

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