# Newton's third law in magnetic in magnetic fields

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?

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

@Jon Custer is right if a magnet producing the magnetic field is present.

But there is more to learn of this question: As Frank Hertz famously discovered, there are so called elector-magnetic waves. These waves are made up of alternating electric and magnetic fields, that are unrelated to any physical object in the classical newtonian sense. This is different to the magnetic field of the magnet.

Since newtons third law is very much equivalent to conservation of momentum I will concentrate on this formulation of Newtons theory.

1. The downfall of classical conservation of momentum: These fields can of course exhibit force on a charged particle with non-zero mass, very much like the magnetic field of the magnet. Therefore the fields are changing the momentum of the particle. This is the downfall of the classical concept of conservation of momentum, since there is no other particle that can assert for the overall change of momentum of the entire system. By classical I mean that momentum is just $$\begin{equation} \mathbf{p}=m\mathbf{v} \end{equation}$$ and therefore only associated with mass. This is the Newtonian view on monentum.
2. Why momentum is still conserved in a broader sense: Experiments have shown that the fields themselves or the electromagnetic wave for that purpose carry momentum themselves. So the change in momentum of the carged particle is compensated by the change of momentum of the electromagnetic wave. To fully understand this concept you shouldy study Maxwell's theory.

Remark: I edited large parts of this answer, as it didn't meet my quality standard anymore and caused misunderstandings in the comment section.

• Remember that a field also carries momentum. Total momentum is conserved a lso in this case. – my2cts Jul 10 '19 at 21:00
• 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. – TheoreticalMinimum Jul 10 '19 at 21:23
• Newton mechanics does not account for electromagnetism at all. The fields are zero. – my2cts Jul 10 '19 at 21:49
• If I could I would downvote both your comments, you're just repeating what I said. – TheoreticalMinimum Jul 10 '19 at 21:52
• Relax @TheoreticalMinimum. – user109018 Jul 10 '19 at 21:55