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?