I recently read Griffiths paper on Hidden momentum, and still didn't found it complete. Following is the short summary.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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

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