Electromagnetic shielding, some simple formulae for closed uniform shields

Electromagnetic shields should be adequate without incurring undue cost or weight. A number of formulas are collected that are consistent with electromagnetic theory. Such formulas will in many cases give shielding estimates quite different from what would be obtained from the use of engineering formulas as presented in widespread handbooks and shielding manuals. The classical, but often distorted, quasistatic formulas for sphere and infinite circular cylinder with internal or external source are complemented by estimates for a finite circular cylinder with closed ends and for the coupling between two (coaxial or coplanar) coils on either side of an infinite plane shield. Formulas and diagrams are also given for double and multiple shields where the shells may be of different materials. In addition to these quasistatic cases, formulas are also given for the penetrating field when a plane wave is (obliquely) incident on an infinite plane shield or an infinite circular cylinder. For each material it is assumed that the relative permeability is much higher than unity.