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Moving magnet and conductor problem by
Ciro Santilli 36 Updated 2025-04-24 +Created 1970-01-01
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!
The solution to this problem is length contraction: the positive charges are length contracted and the moving electrons aren't, and therefore they are denser and therefore there is an effective charge from that frame.
This is also mentioned at David Tong 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".