Ciro Santilli
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Charged particle moving at the same speed of electrons thought experiment | 🗖 nosplit | ↑ parent "Classical electromagnetism and special relativity" | 180

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This is a well known though experiment, which Richard Feynman used to emphasize
  • infinite wire with balanced positive and negative charges, so no net charge, but a net magnetic field
  • a single charge moves parallel to wire at the same speed as the electrons
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In the above experiment:
  • from the wire frame, the charge feels electromagnetic force, because it is moving and there is a magnetic field
  • from the single charge frame, there is still magnetic field (positive charges are moving), but the body itself is not moving, so there is no force!
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The solution to this problem is length contraction: the positive charges are length contracted and the moving electrons aren't, and so therefore they are denser and therefore there is an effective charge from that frame.
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This is also mentioned at David Tong http://www.damtp.cam.ac.uk/user/tong/em/el4.pdf (archive) "David Tong: Lectures on Electromagnetism - 5. Electromagnetism and Relativity" "5.2.1 Magnetism and Relativity".
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Video 46. "How Special Relativity Fixed Electromagnetism" by The Science Asylum (2019-09-11) Source.
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