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In this paper, the authors have calculated the force on the tube, and stated that the magnitude of force on the magnet is same due to Newton's third law.

However, the third law is not valid under the special theory of relativity. In this case, are the forces still equal and opposite in magnitude due to some deeper reason? Is the net momentum carried by the fields is zero in this case?

Or is it just a low speed approximation? In electromagnetism, low speed approximations are not always valid (then magnetic force due to slowly moving charges would not arise)

In case it is a low speed approximation, how to find the force of the magnet on from an inertial frame where the tube is stationary?

Archisman Panigrahi
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  • Does the question have anything to do with the paper specifically, or are you just asking if Newton's third law holds under special relativity? – Doug Jun 12 '18 at 17:15
  • @Doug I have read that Newton's third law is not valid under special relativity. So, I am asking whether the result (force on the magnet) in the paper is exact, and if not, then how to derive it, given that the force in the copper tube has already been found – Archisman Panigrahi Jun 12 '18 at 17:17
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    Why are you invoking special relativity? All the velocities needed here are very small compared to c – Triatticus Jun 12 '18 at 17:28
  • Triatticus is correct, also see https://physics.stackexchange.com/questions/240053/griffiths-argument-that-newtons-third-law-is-invalid-in-special-relativity – Doug Jun 12 '18 at 17:44
  • Are not some momentum stored in the field? I am asking how to find the relativistic exact force, under dipole approximation of magnet – Archisman Panigrahi Jun 12 '18 at 18:12
  • @Triatticus in electromagnetism, the effect of small speeds is not negligible. – Archisman Panigrahi Jun 13 '18 at 03:10

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