# Magnetic Field Penetration Depth in Various Materials and Applications
## 4 Discussion
However, this analysis is extended to include the behavior of magnetic fields in insulating materials and heavy metals, given their relevance. It is essential not to limit the study to the properties of the magnetic field but to consider all factors that can generate new knowledge and evaluate the possible collateral effects that these materials may have on living beings. \(\omega=2\pi\)f is the angular frequency (in radians per second), f is the frequency of the electromagnetic wave (in Hz), \(\mu\) is the magnetic permeability for all materials listed in the table (\(4\pi\times 10^{-7}\) H/m), and \(\sigma\) is the electrical conductivity (in S/m). For this case, a frequency of \(1\times 10^{9}\) Hz was considered, corresponding to high-frequency radio waves, such as those used in telecommunications or radar systems. Magnetic permeability is considered uniform for all materials in Table 6, which is a valid approximation for non-ferromagnetic materials. Electrical conductivities vary significantly, which impacts the penetration depth (\(\lambda\)). The Figure 10 shows that the penetration depth of a magnetic field in heavy metals can reach approximately 10 m, as calculated with Equation (6). This result confirms that, at lower frequencies, the penetration of the magnetic field is greater. The calculations were based on typical values of intrinsic material properties, such as conductivity and magnetic permeability, which determine the degree of field attenuation as a function of frequency. \begin{table}
\begin{tabular}{l l l} \hline
**Materials** & \(\sigma\) **(S/m)** & \(\lambda\) **(m)** \\ \hline Ambient air & \(1\times 10^{-24}\) & \(15\times 10^{9}\) \\ Virgin Teflon & \(1\times 10^{-23}\) & \(5\times 10^{9}\) \\ Mineral mica & \(1\times 10^{-16}\) & \(1\times 10^{9}\) \\ Rubber & \(1\times 10^{-15}\) & \(503\times 10^{3}\) \\ Natural rubber & \(1\times 10^{-15}\) & \(503\times 10^{3}\) \\ Polyethylene foam & \(1\times 10^{-15}\) & \(503\times 10^{3}\) \\ Insulating foam & \(1\times 10^{-15}\) & \(503\times 10^{3}\) \\ Mica sheet & \(1\times 10^{-15}\) & \(503\times 10^{3}\) \\ Porcelain & \(1\times 10^{-14}\) & \(159\times 10^{3}\) \\ Dry wood & \(1\times 10^{-14}\) & \(159\times 10^{3}\) \\ Insulating nylon & \(1\times 10^{-14}\) & \(159\times 10^{3}\) \\ Varnish & \(1\times 10^{-13}\) & \(50\times 10^{3}\) \\ Plastic (generic) & \(1\times 10^{-13}\) & \(15\times 10^{3}\) \\ Glass & \(1\times 10^{-12}\) & \(15\times 10^{3}\) \\ Cardboard & \(1\times 10^{-12}\) & \(15\times 10^{3}\) \\ Paper & \(1\times 10^{-12}\) & \(15\times 10^{3}\) \\ Ceramic earthquake & \(1\times 10^{-11}\) & \(5\times 10^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Depth of penetration of the magnetic field into insulating materials. Figure 10: Penetration depth of (\(\lambda\)) in heavy metals. This information is essential for various applications in engineering, physics, geophysics, and human health. However, it is important to consider that some heavy metals, in addition to their useful properties, are toxic and can cause significant damage to organs such as the brain, kidneys, and liver. The depth of penetration of the magnetic field (ppB, in mm) represents the distance an initial magnetic field (B1, in Teslas) can penetrate a material before attenuating significantly. Figure 11 shows that the magnetic field passing through the material (B2, in Teslas) is significantly lower due to the loss of intensity caused by the intrinsic attenuation of the material. This phenomenon is determined by the material properties, such as conductivity and magnetic permeability, and varies according to the type of material (insulators, semiconductors, heavy metals, superconductors, conductors, and natural materials). Each type of material exhibits unique behavior toward magnetic field propagation, leading to significant differences in B2 values and penetration depth (\(\lambda\)).