2 electromagnetic loops, with light-speed constraints: Is momentum conserved?

[PhysicsProf]

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)

[PhysicsProf]

  PS -- If it is correct that momentum is not conserved, this is the same as saying that Newton's Third Law is violated.  That is, loop C experiences a force to the right while NOTHING experiences a force to the left.  And the result depends on speed-of-light constraints which Newton knew nothing about.  Yes, one could posit "action at a distance", instantaneous forces -- but this would violate light-speed constraints.  Something's gotta give...  but I can't find it.

And experiment would be nice... not easy, but doable I suppose.

IF there is a violation of Newtons' Third Law, then I have thought of a variation on the experiment in which electrons are moved through conductors in a way that violates Lenz's law...  This in turn may result in ou -- so these are important questions.
  Lenz's law is basically a statement on Newton's Third Law:

Lenz's law ... is a common way of understanding how electromagnetic circuits must always obey Newton's third law and The Law of Conservation of Energy.[1] Lenz's law is named after Heinrich Lenz, and it says:

   "An induced current is always in such a direction as to oppose the motion or change causing it"
[snip]
Conservation of momentum

Momentum must be conserved in the process, so if q1 is pushed in one direction, then q2 ought to be pushed in the other direction by the same force at the same time. However, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced (see Retarded potential). This means that for a brief period of time, the total momentum of the two charges are not conserved, implying that the difference should be accounted for by momentum in the fields, as speculated by Richard P. Feynman.[2] Famous 19th century electrodynamicist James Clerk Maxwell called this the "electromagnetic momentum", although this idea is not generally accepted as a part of standard curricula in physics classes as of 2010.[3] Yet, such a treatment of fields may be necessary in the case of applying Lenz's law to opposite charges. It is normally assumed that the charges in question are like charges. If they are not, such as a proton and an electron, the interaction is different. An electron generating a magnetic field would generate an emf that causes a proton to change its motion in the same direction as the electron.

[/b]
http://en.wikipedia.org/wiki/Lenz%27s_law

  This seems correct -- but then the moving particles, electron in one direction and proton in the SAME direction -- appear to be violating conservation of momentum, since both are moving in the same direction.  

Pls note that Newton's Third Law is equivalent to the law of Conservation of Momentum:

F12 = -F21  ::  dPvector1/dt = -dPvector2/dt, so change in Pvector1 = MINUS the change in Pvector2.

You see, I believe I can apply this to a rather simple transformer also, and get violation of Lenz's law ... but I'll save that for a future post as family duties call...  
Ciao

[Grumpy]

There are many discussions of this on the internet.

http://webcache.googleusercontent.com/search?q=cache:UFj62ZyDlHoJ:lofi.forum.physorg.com/Are-All-The-Textbooks-Wrong_18233.html+electron+spin+momentum+not+conserved&cd=11&hl=en&ct=clnk&gl=us&source=www.google.com

About 1/4 of the way down, DaveLush states this, which caught my attention:

The Coulomb force eventually balances things out but in the short term the linear mechanical angular momentum is not conserved.

[PhysicsProf]

  Thanks, Grumpy!   
Read it, and skimmed some of David Lush's papers. 
He appears mostly interested in quantum physics, but my question in electrodynamics might be relevant, as momentum non-conservation is a key issue.

I've written him an email, will see if he can help on the thought experiment I proposed (post 1).

[wattsup]

@PhysicsProf

I can't really picture what is proposed but I really like the term "fringe fields". lol

Also, I posted something about using many diodes to find the best working ones. Do you think this may apply to your tests with your small toroid. If you are in the higher frequency ranges I am sure you will see some major differences. Anyways just food for thought.

wattsup

[BEP]

PhysicsProf,

Can't wait to see your 3 loop idea in a working test.

As far as I know there are three ways to avoid Lenz. The first is having two coils with an orientation that just doesn't produce useful inductive coupling. The second doesn't use direct induction between a primary and secondary. The third requires the use of three planar coils.

The last two are normally denied as not feasible or not functional. Hopefully, your idea will be undeniably feasible and functional 

As far as Coulomb providing the balance...  I doubt it does. I can see where the Coulomb force will conserve energy but not angular momentum for a single direction.
The open loop influenced by an inductive magnetic field will not be repelled but the ends of that loop will be attracted to one another. So I suppose you could say that most of the angular momentum is converted to energy (opposite charges) and then the attraction of those charges is converted to momentum perpendicular to the first (perhaps a tiny percentage of the first?).

Keep in-mind that applying a potential to a loop already enveloped in a magnetic field may decrease or increase the velocity factor, depending upon the current direction and relative polarity of the applied magnetic field.

Unless I'm not visualizing your thought experiment correctly, the problem with such an experiment is in working with single turn loops. In reality, additional loops will skew the results in one way or another just by the type of coil. Unlike the standard statement of 'coil geometry doesn't matter', it does matter a great deal if you are capable of winding something besides a common solenoid style coil.

[PhysicsProf]

Good point,  "fringe field" -- Wattsup

PhysicsProf,

Can't wait to see your 3 loop idea in a working test.

As far as I know there are three ways to avoid Lenz. The first is having two coils with an orientation that just doesn't produce useful inductive coupling. The second doesn't use direct induction between a primary and secondary. The third requires the use of three planar coils.

The last two are normally denied as not feasible or not functional. Hopefully, your idea will be undeniably feasible and functional 

How do you orient the coils for these "three ways, WW?  I'd like to learn your concepts here.

"As far as Coulomb providing the balance...  I doubt it does. I can see where the Coulomb force will conserve energy but not angular momentum for a single direction.
The open loop influenced by an inductive magnetic field will not be repelled but the ends of that loop will be attracted to one another. So I suppose you could say that most of the angular momentum is converted to energy (opposite charges) and then the attraction of those charges is converted to momentum perpendicular to the first (perhaps a tiny percentage of the first?).

Keep in-mind that applying a potential to a loop already enveloped in a magnetic field may decrease or increase the velocity factor, depending upon the current direction and relative polarity of the applied magnetic field.

Unless I'm not visualizing your thought experiment correctly, the problem with such an experiment is in working with single turn loops. In reality, additional loops will skew the results in one way or another just by the type of coil. Unlike the standard statement of 'coil geometry doesn't matter', it does matter a great deal if you are capable of winding something besides a common solenoid style coil.

So far this is a "thought experiment".  To show the question / principle.   If I can understand the physics better, I'm working on a more "testable" version, rather than a single-wire-loop.

Thanks for comments!

[PhysicsProf]

  As mentioned in the first post here, one may add a material M of high magnetic permeability on the Z axis, extending between the loops. 

Now the speed of propagation for the changing B field in this material becomes important. 
In vacuum, a change in the B field -- that "information" -- will propagate at the speed of light. 
But in M, the propagation speed will be less because the dipoles in M must physically move to become more oriented (for an increasing B).  This takes time.
Indeed, the magnetic propagation speed may be much less than c.

OK -- to simplify, take a strong permanent magnet and attach it (very rapidly) to the end of a rod made of nanoperm, no, let's make it iron (so that we might find a speed-value in existing literature).

How fast will the B-field from this magnet travel along the iron?

I think this is an important question -- does anyone know if magnetic-field propagation speeds for various materials have been measured?

[Grumpy]

These may help:

[PhysicsProf]

  Very helpful.  Thanks, Grumpy.

If I understand correctly, roughly a ms (or two) is needed for magnetic flux to penetrate the main core of a laminated core under test.  See attached.
That's a long time, compared to the speed of light!  and suggests a way to get the secondary current to lag the primary current in a transformer -- for instance, by putting primary and 2-ary separated by some distance (eg. 10 cm) on an iron rod.  Having a box-shaped core is another approach, with 1-ary and 2-ary well separated.  Next put an air gap in the box-core....    I've got to try some of these things experimentally, when I get back home.

Man, I've got a lot to learn.

[Grumpy]

If there is a violation of momentum conservation, it may be tough to prove that the system is not acted on by external influences.