I took a look at your solenoid example and found that all the forces on the solenoids cancel out. Here is a picture of the top part of the loop. A similar picture can be drawn for the bottom part of the loop.
Edit: The effect is similar to a compass needle aligning with Earth's magnetic field
There is no change in total momentum. The system gets some momentum, the electromagnetic field gets some momentum, and everybody is happy and Newton's third law is satisfied.
In response to your first two sentences: where does the momentum from an exploding bomb "come from"?
Newton's third law is just another way of saying that momentum is conserved. The crux of the matter is then how momentum is conserved with the Lorentz force. All explanations regarding the conservation of momentum seem to say that the electromagnetic field carries the momentum. The magnets do...
Could you explain the origin of the force back on the magnets in more detail? The wire feels a force due to the Lorentz Force. I've never seen anything saying that the Lorentz force causing an equal but opposite force back on the origin of the magnetic field.
Thanks!
Edit: I would also like to...
The electromagnetic field can be used to transfer momentum. Could this explain what is happening here?
For example, a solar sail uses momentum from photons (electromagnetic disturbances) to accelerate.
Could this be what is happening here?
Edit: Also what is the source of the force that...
Here is a picture of a situation I thought of:
The circles between the magnets indicate a wire with current flowing in the direction given. This picture is a cross section of a loop of wire, looking down. Not included in this picture is the battery and non-conductive connecting materials...