Apparent violation of momentum conservation in EM

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SUMMARY

The discussion centers on the apparent violation of momentum conservation in electromagnetic (EM) systems involving two cylindrical shells with charges +Q and -Q, connected by a wire. As the shells discharge, they experience a magnetic force causing movement in the negative y-direction, while the field momentum indicates a positive x-direction. This discrepancy raises questions about hidden momentum, which is crucial for understanding the conservation laws in this context. A reference to a detailed treatment of hidden momentum is provided for further exploration.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Lorentz force law
  • Familiarity with momentum conservation principles in physics
  • Knowledge of cylindrical coordinate systems and their applications in electromagnetism
  • Basic grasp of magnetic fields and their interactions with charged objects
NEXT STEPS
  • Study the concept of hidden momentum in electromagnetic systems
  • Review the Lorentz force law and its implications for charged particles
  • Examine the principles of momentum conservation in non-inertial reference frames
  • Explore the provided reference on hidden momentum for deeper insights
USEFUL FOR

This discussion is beneficial for physicists, electrical engineers, and students studying electromagnetism, particularly those interested in advanced topics related to momentum conservation and electromagnetic interactions.

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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