**Authors:** Frederick M. Tesche

**Source:** FERMAT, Volume 3, Article 4, May_Jun, 2014

**Abstract:** This paper takes a fresh look at two classical
electromagnetic (EM) shielding problems involving 1) a
time harmonic analysis of a closed, imperfectly
conducting spherical shell and, 2) a quasi-static analysis
of a perfectly conducting hollow sphere with an aperture.
Previous studies of the EM shielding provided by these
geometries have concentrated on evaluating the E- and
H-fields at the center of the shield. While the internal H-field in the shielded volume of the conducting shell is very
close to being constant, the same is not true for the E-field, where there can be a significant variation in the E-field intensity from point to point within the interior.

For both of these canonical shielding problems, the analysis methods are reviewed and are used to determine cumulative probability distributions for the fields within the shielded volume.

In implementing the analysis for the conducting shell, the use of scaled Hankel functions is described. This is used to avoid numerical difficulties in evaluating the spherical harmonic solution for lossy medium. Additionally, closed-form expressions for the wave expansion coefficients in the spherical coordinate system are derived. The analysis of the hollow sphere with an aperture likewise permits the determination of the E-fields anywhere in and around the sphere.

**Index Terms:** EM Shielding, Spherical Shield, Sphere
with Aperture, Spherical Harmonic Expansions, Scaled
Spherical Harmonics.

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