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What cases would a faraday cage of real material (like copper) not block exterior EM radiation like an ideal one made of a perfect conductor? At very high or low frequencies?

How can the design be improved to mitigate those cases?

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    $\begingroup$ See e.g. en.wikipedia.org/wiki/Skin_effect for the case of conductors with finite conductivity, which makes it hard to shield against magnetic AC fields at low frequencies without the use of ferromagnetic materials. The case of high frequency penetration of mesh-like shields or plates with holes is more complicated. $\endgroup$
    – FlatterMann
    Oct 20, 2022 at 8:14

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