Hey, guys. I'm on a long family trip, by car, visiting relatives in Michigan, Maryland, Penna, etc. and away from the lab TOO long. But I've been thinking more about the Faraday paradox and the following -- which also appears to be paradoxical. I posted this question on a physics forum, no response yet.
Can anyone provide an answer?
I'm a retired Physics Professor, and this is an important question to me... but
I admit I'm stumped.... unless I give up the idea that momentum is always conserved in electromagnet devices.... 
Thought experiment I.
Consider two loops of wire, 2 small dipoles B and C , with a common axis z (facing each other) and (say) 30 cm apart B to C. At the speed of light, information (including a change in magnetic field) will require 1 nanosecond to travel from C to B.1. Have the current on in coil B for some period of time at the start, so the B-fields at C is established in the +z-direction.
2. Turn loop B off rapidly (fall time < 0.3 ns, say) at the same time that a current in loop C is turned ON (rapidly, rise time <0.3ns, and opposite sense with respect to the previous current in loop B ).
3. In this way, as the current is turned on in loop C, it is immersed in the field from loop B and therefore both receives an impulse to the right, in the +z-direction.
However, loop B will be "off" (and open so no effective eddy currents) when the "return" field from loop C arrives.
Thus, loop C (which is free to move) will experience an impulse giving it momentum in the +z direction (to the right), whereas loop B will not experience an impulse to the left.I think this argument is sufficiently simple to sketch and to ponder.
Thought Experiment II.
However,
If you argue that there is momentum to the left "in the magnetic field" from loop B, I will add a third loop to the left (call it A), and again, as B is opened rapidly (short fall time) -- at the same time that a current in A is turned ON (rapidly, and SAME sense with respect to the previous current in loop B ).
In this way, loops A and C (both free to move) as they turn on are immersed in the field from B while having currents in the opposite sense -- therefore BOTH loops receive an impulse to the right, in the +z-direction.
Oh, and I will need to turn off the currents in loops B and C rather quickly, so that they both receive impulses in the +z direction without "feeling" the B fields from each other, for they will be "off" when those fields arrive.
If you're concerned about fringe fields, I can add a rod of very high magnetic permeability down the z-axis, extending from A to C, so that essentially all the magnetic field is contained on the z-axis.
Whew -- simple thought experiment, but one that could actually be done IMO.
What will happen? Will there be momentum imparted to the right, but not to the left?
Hey, thanks for thinking about this with me.
- Prof. Jones (Emeritus)
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Topic: 2 electromagnetic loops, with light-speed constraints: Is momentum conserved? (Read 8142 times)
