# Magnetic Field Penetration Depth in Various Materials and Applications
## 1 Introduction
Using the Britannica definition of the magnetic field, the flux lines are known, but it is unknown how much they can penetrate at a certain mass density, magnetic field generation, its range and lines are presented in Figure 1.  
This magnetic field is based on several laws that explain the interactions between currents, fields, and forces: The Ampere-Maxwell Law establishes the connection between direct currents and the static magnetic field (B), while the Biot-Savart Law describes the relationship between an electric current and the resulting magnetic field. [PERSON]'s Third Law deals with magnetic flux through closed surfaces, while the Faraday-Lenz Law links the time variation of a magnetic field to an induced voltage drop. Finally, the Lorentz Force Law and Laplace's Second Law detail how moving charges interact with the magnetic field (B), depending on the current involved. From the 1970s to the present day, research on ppB in conductors, semiconductors, superconductors, and insulators has highlighted its importance for solving everyday problems, such as applications in healthcare and advanced technology. For monocrystalline materials, the temperature and operating frequency are important [15]. [PERSON] discovered superconductors in 1911, materials that conduct electricity without resistance at low temperatures. Elements such as sulfur, boron, and carbon are superconductors under high pressure or in altered forms. The review analyzes the evolution of semiconductors, highlighting innovations, challenges, geopolitics, and economics, including emerging technologies such as graphene [16]. Electronic materials such as metal nitrides are transition materials and an important class of materials with applications as abrasives, semiconductors, superconductors, lithium-ion conductors, and thermoelectrics [17]. In addition, concrete is recycled as a filler in sand-line products and waste. Insulating materials such as glass fiber, rock wool, and reconsidered sand are used as insulating materials [18]. Unlayered 2D materials stand out for their unique properties; e.g., platinum monosulfide is scarcely studied due to its difficult synthesis [19]. The dimensions of electronic and natural materials are illustrated in Figure 2.  
Figure 1: Magnetic field generation, its range, and lines, adapted from [14]. Figure 2: Dimensions of electronic and natural materials, adapted from [16; 2; 17; 18]. These dimensions provide information to take into account in the selection and pursuit of scientific studies, and each of these materials has specific applications according to their electrical, magnetic, or mechanical properties, which makes them useful in different areas of engineering and the sciences. In high Tc cuprate superconductors, the London penetration depth (\(\lambda\)L) first decreases exponentially and then follows a power law due to the disappearance of the energy gap (\(\Delta\)g) [20]. However, ref. [21] determined a lower critical field Hc1 of 0.82 and 0.55 Tesla and a London penetration depth \(\lambda\) of 20 nm and 30 nm in H3S and LaH10, respectively. Then, as illustrated in [22], the coil used in transcranial magnetic stimulation (TMS) requires a balance between several parameters, such as the magnetic flux density (B), inductance (L), induced electric field (E), locality, penetration depth, and coil heating, among others. The importance of this review is to understand the topic on the basis of scientific research from previous centuries to the present day. This phenomenon, called the magnetic field, is widely used in multiple applications. The generation of a magnetic field depends on the modeled matrix design, frequency, types of coils, and other factors. Due to this knowledge gap, there is interest in understanding and controlling the ppB and responding to the need to harness this phenomenon in practical solutions, from water treatment, high-efficiency battery design, wireless energy transport, and tumor detection in the human body to advanced biomedical ones.