Mind boggling attempt to apply Newton's 3rd law

[PhiowPhi]

In classical mechanics, it's pretty straight forward for me to apply it(sometimes...), and really intuitive to picture it. However, when I kick it up a notch... to apply Newton's 3rd law in electrodynamics, my brain malfunctions...

Simplest example I can think of, a conductor carrying a wire placed inside a magnetic field like so:

This diagram shows it all, when current flows in the conductor perpendicular to the magnetic field of the magnet, there is a Lorentz force created. What is the action? The Lorentz force? What is the reaction then... a magnetic force acting on the magnet ?

Another example, instead of using a permanent magnet which has a complexity of it's own(with magnetic moment) let's use two wires like so:

This example I think is easier for me to apply Newton's 3rd law, due to the current flow of each wire and their magnetic fields they both have equal and opposing forces acting on one another? I mean, if the blue wire attracts the green wire, likewise the green wire will attract the blue wire and vice versa in the case of repulsion due to the opposite current flows. So, the Lorentz force is the action and reaction force in such systems?

I've read other thread related to this topic, some members related momentum to this, and how it will be conserved can someone please explain that point too?

 

[lychette]

If the magnet is held in place then the force on the wire will make the wire move, if the wire is a rigid bar (of copper) and the magnet is free to move then the magnet will move due to the force.

 

[PhiowPhi]

If the magnet is held in place then the force on the wire will make the wire move, if the wire is a rigid bar (of copper) and the magnet is free to move then the magnet will move due to the force.

What is the specific reaction force acting on the magnet. Is it a repulsive magnetic force due to the conductor's magnetic field(N/S)?

 

[Dale]

to apply Newton's 3rd law in electrodynamics

Newton's 3rd law doesn't always apply in electrodynamics. Newton's 3rd law is a statement about the conservation of momentum, but the EM field also carries momentum. So you can get situations where mechanical momentum is not conserved because momentum is being transferred from the matter to the fields.

However, if you are in a static situation then Newton's 3rd law will apply because the momentum of the field will be constant.

there is a Lorentz force created. What is the action? The Lorentz force? What is the reaction then... a magnetic force acting on the magnet ?

Yes.

So, the Lorentz force is the action and reaction force in such systems?

Yes.

You may be getting worried about the "action" and "reaction" labels. Those are completely arbitrary. The point is that there is a pair of forces which are equal and opposite. Which one you choose to label as the "action" and the one you choose to label as the "reaction" is a matter of personal taste, not physics.

 

[PhiowPhi]

Newton's 3rd law doesn't always apply in electrodynamics. Newton's 3rd law is a statement about the conservation of momentum, but the EM field also carries momentum. So you can get situations where mechanical momentum is not conserved because momentum is being transferred from the matter to the fields.

That makes sense, because EM fields can carry energy too.