Apparent violation of momentum conservation in EM

AI Thread Summary
The discussion centers on a scenario involving two charged cylindrical shells in a magnetic field, where the shells are discharged and experience a force that causes them to move. Despite the initial symmetry suggesting zero total field momentum, the discharge creates a temporary momentum in the negative y-direction for the shells. This leads to a discrepancy as the field momentum points in the positive x-direction, raising questions about momentum conservation. The concept of "hidden momentum" is introduced as a potential explanation for this apparent violation. A reference is provided for further exploration of the topic.
Carnimel
We have two cylindrical shells (with radii a and b and charges +Q and -Q) along the z-axis. There is a uniform magnetic field (in the positive z-direction) out to radius r from the z-axis. Because of the symmetry, the total field momentum is zero. Suppose we now connect the shells using a wire along the positive x-direction. The shells are slowly discharged. The magnetic force will move the shells along the negative y-direction (at least temporarily). If we stop the discharge shortly after that, the shells will have a momentum to the negative y-direction but the field momentum will point in the positive x-direction (due to the sliver of unbalanced momentum in the region to the positive y-direction). What did I miss?
 
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Thank you for the reference! I will look into it.
 

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