Why Does a Charged Box Exhibit Higher Inertia Due to Mass-Energy Equivalence?

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Discussion Overview

The discussion centers around the concept of inertia in a charged metallic box, specifically exploring how mass-energy equivalence relates to the energy stored in the electric field of the box. Participants consider thought experiments to illustrate why a charged box may exhibit higher inertia compared to an uncharged one, touching on concepts of electromagnetic radiation and momentum.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant claims that a charged box has a higher energy content due to the electric field, leading to a higher rest mass and greater resistance to acceleration.
  • Another participant questions the initial description and seeks clarification on the thought experiment related to the acceleration of a charged box.
  • A different viewpoint suggests that accelerating a charged box produces electromagnetic radiation, and the outgoing momentum of this radiation must be balanced by an additional force to push the box.
  • One participant references historical attempts to address this issue in the 19th century, indicating that previous models did not yield satisfactory results and expressing skepticism about separating charge from the field in terms of mass allocation.

Areas of Agreement / Disagreement

Participants express differing views on the mechanisms at play regarding the inertia of a charged box, with no consensus reached on the validity of the proposed thought experiments or the historical context referenced.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about mass allocation in systems involving electric fields and the complexities of electromagnetic radiation, which remain unresolved.

andreabalestrero
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A charged, metallic box has an energy content higher than an uncharged box, due to the energy stored in the electric field (which is equal to the work that has to be done to bring the charges from "infinity" to the surface of the box). So, due to the mass-energy equivalence, a charge box has a higher rest mass, and it will offer a higher resistance when accelerated. Is there a thought experiment that could explain why a charged box is harder to accelerate?
 
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andreabalestrero said:
Is there a thought experiment that could explain why a charged box is harder to accelerate?
Didn't you just describe one?
 
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Actually, I was thinking something like that accelerating a charged box will produce EM radiation, and somehow the outgoing momentum of the radiation results in a force to be balanced to push the box
 
This was attempted in the 19th century. It did not work out. You get 4/3 = 1 and similar nonsense.

You cannot separate the charge from the field and say "this much mass is over here and that much mass is over there", just as you can't allocate the mass of a system of photons to each individual, yet massless, photon.
 
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