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I've been told both are true, but it confuses me on what is actually happening and what is carrying charge in the wire itself. Length contraction would be almost nothing at the speeds at which electron drift happens. For it to be true I'd think then charge must be carried by something at a very fast speed. There are a lot of electrons moving, the length contraction creates more charge in the same space to the inertial reference frame, and you feel a charge based push perpendicular to the motion of the electrons, is how it is explained to me. I know I'm not understanding something or one explanation was wrong but after looking and not finding any good answers I figured I'd ask here. Thank you for your help in advance.

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    It's not clear to me what the conflict is between length contraction and electron drift velocity. Could you spell it out more clearly? – psitae Jan 23 '19 at 22:28
  • for more charge to be in the same space via length contraction, you'd need a high speed (10% the speed of light to get a 200 ft object to appear to be 199 ft), but electron drift is very slow (like .25mm a second slow). So my confusion is how would almost immeasurable length contraction result in a magnetic like force. I am not understanding something, there's other complications, or one explanation is wrong. –  Jan 23 '19 at 22:34
  • It seems like you're assuming that length contraction is the only thing that can make a magnetic field. But a changing E field is what makes a B field. – psitae Jan 23 '19 at 22:38
  • ... there can't be a net force perpendicular to the motion of the current in the wire if there isn't a change in charge density, this was the given explanation for that force that is real from a relativistic explanation. The more Maxwell interpretation just states what you said. See https://physics.stackexchange.com/q/71099/ –  Jan 23 '19 at 22:39

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The length contraction is small but the charge of the electrons in a length of copper wire is huge. So the Coulomb force between parallel wires becomes measurable in a frame moving together with the electron drift velocity.

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    That makes sense. Since you gave an answer I'll assume you're pretty sure on that is the explanation. Thank you. –  Jan 23 '19 at 22:45
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    @Wolfe I found this one of the most beautiful things that I learned in my electromagnetism class 40 years ago. The relativistic effect is strong enough to drive electrical trains and lots of other stuff. –  Jan 23 '19 at 23:19