Apparent violation of momentum conservation in EM

In summary, two cylindrical shells with charges +Q and -Q and radii a and b are placed along the z-axis. A uniform magnetic field exists out to radius r from the z-axis in the positive z-direction. Due to symmetry, the total field momentum is zero. When the shells are connected by a wire along the positive x-direction and slowly discharged, the magnetic force causes them to move along the negative y-direction temporarily. If the discharge is stopped shortly after, the shells will have a momentum in the negative y-direction while the field momentum will point in the positive x-direction due to the unbalanced momentum in the region towards the positive y-direction. "Hidden momentum" is a concept that explains this phenomenon, and a detailed explanation can
  • #1
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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  • #3
Thank you for the reference! I will look into it.
 

FAQ: Apparent violation of momentum conservation in EM

What is momentum conservation in electromagnetic (EM) interactions?

In physics, momentum conservation refers to the principle that the total momentum of a closed system remains constant over time. This means that the total momentum of all objects involved in an interaction before and after the interaction must be the same.

What is an apparent violation of momentum conservation in EM?

An apparent violation of momentum conservation in EM refers to situations where the measured momentum of an object before and after an interaction does not appear to be conserved. This can occur in certain EM interactions, such as photon absorption or emission, where energy and momentum may be exchanged between particles.

Why does momentum conservation appear to be violated in some EM interactions?

In certain EM interactions, the energy and momentum of particles may be exchanged in a way that is not immediately apparent. For example, in photon absorption or emission, the momentum of the photon may not be directly measurable, leading to the appearance of a violation of momentum conservation.

How is momentum actually conserved in EM interactions?

In EM interactions, momentum is conserved through the exchange of virtual particles. These particles, such as virtual photons, carry energy and momentum between interacting particles, allowing for momentum to be conserved overall. These virtual particles are not directly observable, which is why the conservation of momentum may not be immediately apparent.

How does the apparent violation of momentum conservation in EM affect our understanding of the laws of physics?

The apparent violation of momentum conservation in EM does not actually contradict the laws of physics. It simply means that our understanding of these laws needs to be expanded to include the concept of virtual particles and their role in momentum conservation. This highlights the ongoing nature of scientific discovery and the need to constantly refine and expand our understanding of the world around us.

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