Understanding the Shielding Efficiency of a Faraday Grid Cage: A spectral domain approach

The static shielding properties of Faraday wire cages are intuitive as for a small mesh size, the effect on the field can be expected to approach that of an ideal Faraday cage, i.e., a closed conductive surface. However, as it has been recently pointed out, the shielding efficiency is somewhat worse than one might expect and does not particularly conform to the simple approximation of an exponentially decaying field, as it is, e.g., described in
The Feynman Lectures on Physics
. In the present contribution, we use the case of a circular 2D wire cage to illustrate how the residual field inside such a cage can be visualized in terms of a spatial spectral consideration of the induced charge. It is shown how the residual field in the cage’s center is related to a single Fourier coefficient of this spectral expansion, and that the approximation of the induced charge as a sampled version of the induced charge of a corresponding ideal Faraday cage yields useful approximations for the residual fields close to the cage boundary. The latter also turn out to justify the exponential decay approximation, at least in this region.