Exploring Newton's Third Law in an Imaginary Magnetic Field

[pays_fan]

Hi, here's a theoretical problem that I am trying to find a satisfactory answer for.

Imagine a coil that is temporarily switched on an off and generates a magnetic field that permeates through space. Now imagine a charged particle passing through this field, at time that the coil is already switched off, and experiencing electromagnetic force. I would assume that the coil would not experience a reactive force because it is switched off (or for the sake of argumentation, it can even be disassembled by the time the charged particle experiences the magnetic field). How is this in line with Netwon's third law?

 

[Orodruin]

a magnetic field that permeates through space

The word ”propagates” would probably be a better fit for what you want to say here. To permeate can also be taken to mean to exist everywhere.

If I understand your question correctly, you want to consider the a field pulse that propagates outwards and is of finite extent in time.

In an interaction with the electromagnetic field, Newton’s third law holds locally for the interaction between the paricle and the field itself. The electromagnetic field carries energy and momentum. This is described by the electromagnetic stress energy tensor. Newton’s third law also holds for the interaction between the coil and the field when the pulse was generated.

 

[bob012345]

In an interaction with the electromagnetic field, Newton’s third law holds locally for the interaction between the particle and the field itself. The electromagnetic field carries energy and momentum. This is described by the electromagnetic stress energy tensor. Newton’s third law also holds for the interaction between the coil and the field when the pulse was generated.

Yes, Feynman showed an example in his Lectures on Physics Volume II page 26-5 fig 26-6 that two charged particles can move in such a way that their forces are not always equal and opposite.

Fig. 26–6. The forces between two moving charges are not always equal and opposite. It appears that “action” is not equal to “reaction.”

https://www.feynmanlectures.caltech.edu/II_26.html

 

[tech99]

If the charge is in the radiated field from the magnet then it will experience an accelerating force. It seems to me that it will radiate a new wave opposing the incoming wave, in the manner of a conductor.

 

[tech99]

Radiation by the magnet implies that the magnet has a finite length. If the charge is very close to such a magnet, it will primarily experience the induction field of the magnet and so it is different to the case for the radiation field. When the current is turned off, the charge will now be in the E field caused by the collapsing magnetic field, and will experience a force. As far as I can see, this force will react directly on the magnet with zero propagation delay.