# EM Momentum,Hidden Momentum,Centre of Energy Theorem and Lorentz Force

1. Apr 8, 2014

### universal_101

I recently read Griffiths paper on Hidden momentum, and still didn't found it complete. Following is the short summary.

The usual setup of current carrying loop and a charge lying nearby, according to the paper, Shockley and James presented the problem, that is, when we let the current die down then according to Maxwell's Equations there is a force on the nearby charge due to the induced electric field, but the same Maxwell's Equations do not predict a reaction force on the loop, and therefore there is a problem.

Now Shockley and James suggested that there is a hidden momentum in the current carrying loop so as to respect momentum conservation, and the Griffiths paper suggests that, since there is Electromagnetic momentum involved in the setup when the current is flowing, there must be some other momentum too in order to balance the EM momentum, otherwise the center of Energy Theorem from SR would be violated.

And Griffiths shows that this other momentum is hidden momentum from the Shockley and James Paper and is exactly equal and opposite to the EM Momentum. And shows that, this EM momentum is the same, which the charge would acquire when the current dies down.

And the hidden momentum is characterized as relativistic mechanical momentum, which is balanced by the EM Momentum, and when we let go the current, the EM momentum goes into the point charge whereas the hidden momentum comes into being and ends up moving the loop in opposite direction and therefore the reaction force. Therefore all the problems solved!

Well not quite, Remember that EM momentum is per unit volume, so we have non-zero EM momentum wherever E and B are perpendicular, in other words EM momentum is spread all over the volume, whereas hidden momentum is associated with the moving charges in the current carrying loop. So, how-come the momentum associated with moving point charges in presence of an E field is balanced by the momentum spread all over the volume.

Secondly, if hidden momentum is mechanical, how-come the loop is not moving already, that is, what kind of mechanical momentum does not produce motion, this is unacceptable physics.

Thirdly, we still don't have the solution to the original problem, that is, Maxwell's equations still do not predict back reaction force from the charge on the loop when current is changing. Ofcourse considering that the situation is well under the domain of the Maxwell's equations.

I think it is one thing to suggest that quasi-static fields carry momentum without moving anything, and entirely different and possibly wrong that mechanical momentum can also exist without having any net motion.

2. Apr 8, 2014

### Bill_K

This paper debunks the idea of "hidden momentum."

3. Apr 9, 2014

### universal_101

This is worse than the hidden momentum itself, that is neglecting the consequences of Center of Energy theorem for EM momentum. I mean it does not seem like a solution to the problem, rather it is a denial of the problem, that Maxwell's Equations don't predict the back reaction force on the changing current loop.

4. Apr 9, 2014

### Meir Achuz

Yes............

5. Apr 10, 2014

### universal_101

And that seems quite a big problem, and the problem becomes of utmost importance if Maxwell's equations are supposed to represent the classical electrodynamics, and it suggests that Maxwell's equations are necessarily incomplete.

6. Apr 10, 2014

### clem

There is NO "back reaction force on the changing current loop."

7. Apr 10, 2014

### universal_101

Yes, but there is NO back reaction force experimentally or theoretically/principally?

That is, how do you get to upheld local momentum conservation if there is NO back reaction Force?

8. Apr 10, 2014

### clem

[/PLAIN] [Broken]
"http://arxiv.org/abs/1302.3880" [Broken]
This paper[/URL] debunks the idea of "hidden momentum.

Last edited by a moderator: May 6, 2017
9. Apr 10, 2014

### clem

That is why and how EM momentum is introduced in textbooks.

10. Apr 10, 2014

### universal_101

Agreed, But you cannot use EM momentum for both conditions, that is, first when the charge is not moving there is EM momentum present, and second when this same EM momentum comes up in the changing current loop while charge is moving and experiencing Lorentz Force.

So basically, instead of having a back reaction force, we are expecting quasi-static EM fields to have momentum, and we are directly associating this momentum to the momentum that the loop would gain. Well then, that is NO more than a trick, for atleast we must know how this supposed EM Momentum is getting transferred to the loop, according to Maxwell's Equations, right? Because the whole setup is well under the domain of classical mechanics.

So I think, it does not matter from where we bring in the momentum for loop to have, but we must accommodate that in Maxwell's equations, to show that there is a back reaction Force.

11. Apr 10, 2014

### Meir Achuz

The loop has NO momentum, and Maxwell's equations show there is NO back reaction force.
The momentum is in the EM field, not the loop.
Did you read the reference Bill K. suggested?

12. Apr 11, 2014

### universal_101

Are you suggesting that EM momentum which can be present in a non-moving system, is the one that gets transferred to the moving charge ? Therefore all problems solved!

Yes I did read the reference, and it clearly says that, center of energy theorem does not apply to EM momentum, how convenient is that.

13. Apr 11, 2014

### Meir Achuz

1. In that reference, an external force holds the charge in place, and produces the EM momentum.
Without the external force the charge would acquire momentum, and the sum of its momentum and the EM momentum would be zero, conserving momentum. That is precisely how textbooks introduce EM momentum.
2. That reference SHOWS "that the center of energy theorem does not apply to EM momentum".

14. Apr 12, 2014

### universal_101

The external force that keep charge stationary w.r.t the loop, supposedly produces the EM momentum when setting up the static charge-current setup. So, does it mean that, if there were NO external force there would not be any EM momentum ?

I think it is time to make it little bit neat,

1.) The current carrying loop never experiences a back reaction force, all the momentum and force exchange is between 'EM Momentum' and the charge. Correct?

2.) If we use external forces to setup the static charge-current experiment, the system has non-zero net momentum in the form of EM Momentum. Correct?

3.) And when we let the current die down, this net EM momentum produces net momentum in the form of the Lorentz Force on the charge. Correct?

Answers to the above assertions would most certainly help me understanding your position on the matter. Thanks

15. Apr 12, 2014

### Meir Achuz

"The external force that keep charge stationary w.r.t the loop, supposedly produces the EM momentum when setting up the static charge-current setup. So, does it mean that, if there were NO external force there would not be any EM momentum?"

No. In the absence of an external force to hold the charge in place, the charge would acquire momentum and the EM field would acquire equal and opposite momentum. The total momentum would then be zero, conserving momentum.
The answers to 1, 2, and 3 are all yes.

16. Apr 12, 2014

### universal_101

But how come you get to choose when to use 'conservation of angular momentum' and when to not use, that is, in one case you have net momentum(EM) and nothing is moving and nobody complains about the violation of conservation of momentum, whereas in the other situation, when the current dies down and charge starts moving, you chose to use conservation of momentum to cancel the EM momentum by the mechanical momentum of moving charge(due to Lorentz force).

17. Apr 12, 2014

### Meir Achuz

External force = rate of change of momentum.
1. With no external force the mechanical momentum of the charge and the EM momentum add up to zero, conserving momentum.
2. With an external force holding the charge in place,tum the external force produces the EM momentum by
F=dP/dt.
3. If the current dies down (after (2) above), the EM momentum is transferred to the charge, conserving momentum.

18. Apr 13, 2014

### universal_101

Well the point is, the system with net non-zero momentum has the non-moving center of energy. That is, there is NO way to detect the EM Momentum, it is abstract in a sense that, it is supposed to be there but nothing is moving.

19. Apr 13, 2014

### Meir Achuz

Your question (3) detects EM momentum when it is transferred to the charge.
What is detection? Do you want to hold it in your hands?
That is how neutrinos are detected.
EM momentum is as real as neutrinos.

20. Apr 13, 2014

### universal_101

Well, just do an experiment and show me, that while the charge is moving the loop is stationary, and then it can be considered as a detection of EM momentum.

Just do the simple experiment, and show us that a part of a charge-current system can move spontaneously when the current dies down, without moving any other part of the system, and may be it would be believable that center of energy theorem does not apply to EM Momentum.

Last edited: Apr 13, 2014