## 6 Numerical Results  
We first consider a copper disk (conductivity \(\sigma=5.7\times 10^{7}\) S/m) with thickness \(d=1\) mm and radius \(a=1.5\) m in a frequency range from 100 Hz to 1 MHz. The electromagnetic source consisting of a circular current loop coaxial with the disk is assumed to be placed at height \(h=30\) cm (i.e., \(h/a=0.2\)) and with a radius \(R=5\) cm (i.e., \(R\ll a\)). In Figure 4, the magnetic shielding effectiveness \(\text{SE}_{\text{H}}\) is evaluated at a symmetric point with respect to the loop position, i.e., at \(z=-h\), and is reported as a function of the frequency. We have used different formulations here; in particular, it can be seen that the formulation based on Mitzner GBCs (see Section 4, _blue solid line_) is perfectly superimposed with respect to the proposed formulation based on the new boundary condition (34) (see Section 5, _cyan dashed-square line_) in the entire frequency range; these results coincide with those obtained with FEKO commercial software (not reported here). On the other hand, the formulation based on the thin-screen approximation [23] (_red dashed line_) is correct only up to about 5 kHz; in this low frequency range, the SE\({}_{\rm H}\) is essentially that of an infinite metallic screen having the same thickness of the disk [18; 19; 20], which is reported in Figure 4 as a dot-dashed line for a fair comparison. In practice, at low frequencies and for the considered values of \(R\) and \(a\) the metallic disk is seen by the loop as if it were of infinite extent. At high frequencies (that is, larger than 100 kHz), all the formulations (i.e., the full Mitzner BC formulation, the new proposed BC formulation, the thin-screen formulation, and FEKO) approach the PEC disk results [14], which are shown in Figure 4 as a dotted line. However, it can clearly be seen that there exists an intermediate frequency range in which neither the thin disk formulation nor the infinite metallic disk formulation can reproduce the correct results. In such a frequency range, the finite thickness of the disk must be carefully taken into account either through the formulation based on Mitzner GBCs or the new boundary condition (34). It can be observed that in this intermediate frequency range the SE\({}_{\rm H}\) of the infinite solid conductive thick screen and the SE\({}_{\rm H}\) of the infinitesimally thin PEC disk are comparable; moreover, the SE\({}_{\rm H}\) of the thick disk with finite conductivity can be much larger (almost 30 dB larger) than the SE\({}_{\rm H}\) of the equivalent PEC disk, presenting a sharp peak. In Figure 5, the dependence of SE\({}_{\rm H}\) on the thickness-to-skin depth ratio \(d/\delta\) is reported for the same parameters as in Figure 4. As expected, the thin disk formulation is accurate only for disk thicknesses smaller than the skin depth \(\delta\). Moreover, in this low-frequency range there is no difference with the infinite solid conductive thick screen. The dependence of SE\({}_{\rm H}\) on the on the source-to-screen distance \(h\) is instead shown in Figure 6. The distance \(h\) ranges from \(h=20\) cm (i.e., \(h/a=0.13\)) to \(h=1.5\) m (i.e., \(h/a=1\)). Thus, it can be seen that a peak of SE\({}_{\rm H}\) may or may not be present in the intermediate frequency range, depending on \(h\); furthermore, the asymptotic PEC limit is approached faster as \(h\) increases. Therefore, the presence of the intermediate frequency range with the presence of the SE\({}_{\rm H}\) peak is strongly dependent on the source-to-screen distance \(h\). It is interesting to point out that at low frequencies the SE\({}_{\rm H}\) increases for larger values of \(h\), while in the high-frequency range the SE\({}_{\rm H}\) dramatically decreases with increasing \(h\). Figure 4: Magnetic shielding effectiveness SE\({}_{\rm H}\) as a function of frequency for a purely conductive disk with parameters \(d=1\) mm, \(a=1.5\) m, and \(\sigma=5.7\times 10^{6}\) S/m (copper).