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Say I have a charged particle moving through a magnetic field perpendicular to it. It will experience a force, but according to Newton third law

Every force has an equal and opposite reaction.

So what is the opposite reaction/force of this magnetic force. Which body experiences this force?

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    $\begingroup$ Not surprisingly, the magnet generating the magnetic field in question. $\endgroup$ – Jon Custer Jul 10 at 19:31
  • $\begingroup$ @JonCuster Keep a compass near a conducting wire. The dial will start rotating, but I think it doesn't just start moving...... $\endgroup$ – user235329 Jul 10 at 19:38
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Jon Custer is right if a magnet producing the magnetic field is present.

But imagine a more interesting case: an electromagnetic wave hitting a charged particle in empty space. The particle experiences a force due to the em fields. Which body experiences the reactio? Clearly, none, since there are no other bodies present. Does this violate newtons third law? Clearly, YES.

Newton's Theory is concerned with the interaction between physical bodies, not with fields. Newton did not know about such thing as a electromagnetic wave or a electromagnetic fields. His theory can not cope with such thing. Eventhough @my2ct pointed out that this is trivial for a physicist it's worth noting for anyone starting to do physics. Any theory has it's limitations.

On a side note: You could ask, is at least momentum conserved? The answer is yes. One might ask "how can this be, there are no other bodies around, clearly conservation of momentum must be broken when the charge just starts moving. You're claims are nonsense!"

In the newtonian world this critcism is valid. But in a more refined theory, the one of classical electromagnetism, we assign momentum to the electromagnetic field itself.

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  • $\begingroup$ Remember that a field also carries momentum. Total momentum is conserved a lso in this case. $\endgroup$ – my2cts Jul 10 at 21:00
  • $\begingroup$ my2cts as is already said in my answer. but a field definitely carries no momentum in the classical newtonian sense, what even is a field in newtonian sense? This is what I tried to bring across, the framework of newtonian mechanics can not describe such phenomena. $\endgroup$ – TheoreticalMinimum Jul 10 at 21:23
  • $\begingroup$ Newton mechanics does not account for electromagnetism at all. The fields are zero. $\endgroup$ – my2cts Jul 10 at 21:49
  • $\begingroup$ If I could I would downvote both your comments, you're just repeating what I said. $\endgroup$ – TheoreticalMinimum Jul 10 at 21:52
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    $\begingroup$ Relax @TheoreticalMinimum. $\endgroup$ – Charles Jul 10 at 21:55

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