# Magnetic Field Penetration Depth in Various Materials and Applications
## 5 Conclusions  
Magnetic permeability (\(\mu=4\pi\times 10^{-7}\) H/m) is considered uniform in conducting, superconducting, natural, insulating, and heavy metal materials. However, variations in electrical conductivity (\(\sigma\)) significantly influence the penetration depth of the magnetic field (\(\lambda\)), which varies from 12 nm to 15,915,494 km, depending on the attenuating material.  
When substituting values into the equations, errors can arise in the units of \(\lambda\), such as expressing them in meters per second instead of meters. It is, therefore, essential to respect the International System of Units (SI) to ensure accuracy in calculations and facilitate subsequent experimental studies.  
In conductive materials, the penetration depth of the magnetic field is low due to the rapid attenuation caused by eddy currents. This effect is particularly noticeable in metals such as copper, where, at a frequency of 60 Hz, \(\lambda\) reaches approximately 8 mm.  
The analysis shows that, in natural materials, the penetration depth of the magnetic field varies between 29 and 91,888,149 m due to the absence of eddy currents. In dielectric materials, such as water and ceramics, the magnetic field is moderately attenuated, allowing greater penetration, although the ionized conductivity of water can generate minimal attenuation.  
In heavy metals, the methodology applied according to Equation (6) indicates that the magnetic field penetration can reach up to 10 m, decreasing with increasing frequency. This phenomenon, determined via conductivity and magnetic permeability, has relevant applications in engineering, physics, and health; however, heavy metals can pose toxic risks to vital organs.  
In insulating materials, the absence of free charges prevents the generation of eddy currents or significant attenuations, allowing the magnetic field to pass almost completely through them, regardless of frequency. The analysis indicates that \(\lambda\) in these materials varies between 5 and 168 m.  
The correlation coefficient of \(-0.324\) between the variables \(\lambda\) (penetration length in nanometers) and Tc (critical temperature in Kelvin) indicates a weak negative relationship, i.e., as Tc increases, \(\lambda\) tends to decrease slightly. The \(p\)-value of 0.081, compared to the 5% significance level (\(\alpha=0.05\)), suggests that the observed relationship is not statistically significant. This means that there is no linear correlation between \(\lambda\) and the critical temperature. This has applications in engineering, such as communications and geophysical exploration; in health, in biomedical therapies; and in physics, in the design of superconducting devices.  
Conceptualisation, P.P.A.G.; methodology, P.P.A.G.; software, W.M.Z.Z.; validation, W.M.Z.Z.; formal analysis, P.P.A.G.; research, P.P.A.G.; resources, E.V.P.; data preservation, E.V.P.; drafting (original draft, review, and editing), P.P.A.G.; visualization, G.E.O.C.; supervision, G.E.O.C.; project management, R.A.F.V. All authors have read and agreed to the published version of the manuscript.  
This review research did not receive external funding, however, for payment of the APC it is possible that the Universidad Nacional Intercultural Fabiola Salazar Legua de Bagua may fund extemporaneously.  
We are grateful to the Universidad Nacional Intercultural Fabiola Salazar Legua de Bagua for providing support for scientific research courses, as this manuscript is a product of it.  
The authors declare that they have no conflict of interest.