Faraday cage

Shielding properties of a metallic, closed box result from so-called Gauss's law. It says that the flux of the electrical field E across a closed surface S is determined by the sum of the electrical charges inside q :

where e₀ is the dielectric permeability of vacuum.

In other words, if inside a closed Gauss surface no electrical charges are present, the net electrical field flux across this surface is zero.

. Let us invert the reasoning: the electrical charges outside the closed surface create a zero flux across this surface. As a result, the fields which have sources outside the surface can not induce charges inside Faraday's cage - the radio receiver or a cell phone are mute inside the box.

In real life, alternate electric fields, in particular at high frequencies, can partially penetrate inside non-perfectly closed surfaces. So, it can happen that the cell phone inside a metal sieve would ring, but in a perfect metal box - it should not.