Faraday cage from Gauss' law alone?

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SUMMARY

The discussion centers on the derivation of the properties of a Faraday cage using Gauss' law. Participants express skepticism regarding derivations that conclude the electric field (E field) inside the cage must vanish solely from a vanishing flux. More robust derivations incorporate both Gauss' law and closed line integrals, leading to the conclusion that the E field inside the cavity is indeed zero. The conversation references an article from SIAM News that explores the complexities surrounding the Faraday cage concept.

PREREQUISITES
  • Understanding of Gauss' law in electrostatics
  • Familiarity with electric field concepts
  • Knowledge of closed line integrals in vector calculus
  • Basic principles of electrostatics and conductors
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  • Read the SIAM News article on Faraday cages for deeper insights
  • Study the mathematical derivation of Gauss' law
  • Explore applications of closed line integrals in electromagnetism
  • Investigate alternative methods for analyzing electric fields in conductors
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Physicists, electrical engineers, and students studying electromagnetism who seek to understand the theoretical foundations and practical implications of Faraday cages.

greypilgrim
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Hi.

Is it possible to derive the properties of a Faraday cage from Gauss' law alone? I found some "derivations" which I find rather unconvincing since they somehow conclude from a vanishing flux that the E field must vanish as well.
Some slightly more elaborate derivations use a combination of Gauss' law and a closed line integral along a path partly inside the cavity and partly inside the conductor. Since all those integrals vanish, the E field inside the cavity must vanish as well, they conclude.

Does this really cover all possible cases?
 
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