# Magnetic Field Penetration Depth in Various Materials and Applications
## 3 Results
### Penetration Depth
\begin{table}
\begin{tabular}{l c c c c} \hline
**Type II Superconductor** & **m (kg)** & \(\rho\)s (m\({}^{-3}\)) & \(\lambda\) (nm) & **Tc (K)** \\ \hline NbTi & 1.18422 \(\times\) 10\({}^{-30}\) & 5 \(\times\) 10\({}^{27}\) & 86 & 9.2 \\ NbTa & 1.00203 \(\times\) 10\({}^{-30}\) & 4 \(\times\) 10\({}^{27}\) & 88 & 10.8 \\ NbSe\({}_{2}\) & 1.27531 \(\times\) 10\({}^{-30}\) & 3 \(\times\) 10\({}^{27}\) & 115 & 7.2 \\ NbReN & 1.18422 \(\times\) 10\({}^{-30}\) & 2.8 \(\times\) 10\({}^{27}\) & 115 & 16.4 \\ MgB\({}_{3}\) & 1.27531 \(\times\) 10\({}^{-30}\) & 2 \(\times\) 10\({}^{27}\) & 141 & 39 \\ NbN & 1.4575 \(\times\) 10\({}^{-30}\) & 2 \(\times\) 10\({}^{27}\) & 150 & 16.2 \\ YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{x}\) (x = 6.92) & 3.64375 \(\times\) 10\({}^{-30}\) & 3 \(\times\) 10\({}^{27}\) & 194 & 92 \\ HoBa\({}_{2}\)Cu\({}_{4}\)O\({}_{8}\) & 3.18828 \(\times\) 10\({}^{-30}\) & 2.5 \(\times\) 10\({}^{27}\) & 199 & 80 \\ YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\delta}\) & 3.18828 \(\times\) 10\({}^{-30}\) & 2.5 \(\times\) 10\({}^{27}\) & 199 & 93 \\ GdBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-\delta}\) & 3.18828 \(\times\) 10\({}^{-30}\) & 2.5 \(\times\) 10\({}^{27}\) & 199 & 92 \\ NdFeAsO\({}_{0.65}\)F\({}_{0.35}\) & 1.36641 \(\times\) 10\({}^{-30}\) & 1 \(\times\) 10\({}^{27}\) & 206 & 51 \\ HFNC & 1.82188 \(\times\) 10\({}^{-30}\) & 1.3 \(\times\) 10\({}^{27}\) & 208 & 25.5 \\ HTSC & 3.64375 \(\times\) 10\({}^{-30}\) & 2.5 \(\times\) 10\({}^{27}\) & 213 & 90 \\ LaFeAsO & 1.82188 \(\times\) 10\({}^{-30}\) & 1.2 \(\times\) 10\({}^{27}\) & 217 & 26 \\ Li\({}_{2}\)Pd\({}_{3}\)B & 2.27735 \(\times\) 10\({}^{-30}\) & 1.5 \(\times\) 10\({}^{27}\) & 217 & 8 \\ Pr\({}_{2-x}\)Ce\({}_{x}\)CuO\({}_{4-\delta}\) & 2.73282 \(\times\) 10\({}^{-30}\) & 1.5 \(\times\) 10\({}^{27}\) & 238 & 27 \\ CaKFe\({}_{4}\)As\({}_{4}\) & 3.18828 \(\times\) 10\({}^{-30}\) & 1.5 \(\times\) 10\({}^{27}\) & 257 & 35 \\ Sr\({}_{0.89}\)La\({}_{0.11}\)CuO\({}_{2}\) & 2.73282 \(\times\) 10\({}^{-30}\) & 1.2 \(\times\) 10\({}^{27}\) & 266 & 40 \\ La\({}_{1.85}\)Sr\({}_{0.15}\)CuO\({}_{4}\) & 2.73282 \(\times\) 10\({}^{-30}\) & 1.2 \(\times\) 10\({}^{27}\) & 266 & 38 \\ Nd\({}_{1.85}\)Ce\({}_{0.15}\)CuO\({}_{4}\) & 2.73282 \(\times\) 10\({}^{-30}\) & 1.2 \(\times\) 10\({}^{27}\) & 266 & 25 \\ BaFe\({}_{2}\)(As\({}_{1-x}\)P\({}_{x}\))\({}_{2}\) (x = 0.3) & 2.73282 \(\times\) 10\({}^{-30}\) & 1 \(\times\) 10\({}^{27}\) & 291 & 30 \\ Na\({}_{x}\)CoO\({}_{2}\) y H\({}_{2}\)O & 1.82188 \(\times\) 10\({}^{-30}\) & 5 \(\times\) 10\({}^{26}\) & 336 & 4.5 \\ Ba\({}_{8}\)Si\({}_{46}\) & 1.82188 \(\times\) 10\({}^{-30}\) & 5 \(\times\) 10\({}^{26}\) & 336 & 8 \\ Na\({}_{2}\)Cs\({}_{61}\) & 2.27735 \(\times\) 10\({}^{-30}\) & 6 \(\times\) 10\({}^{26}\) & 343 & 29 \\ K\({}_{3}\)C\({}_{60}\) & 2.73282 \(\times\) 10\({}^{-30}\) & 7 \(\times\) 10\({}^{26}\) & 348 & 18 \\ Rb\({}_{3}\)C\({}_{60}\) & 2.27735 \(\times\) 10\({}^{-30}\) & 5 \(\times\) 10\({}^{26}\) & 376 & 30 \\ \(\kappa\)-(BEDT-TTF)\({}_{2}\)Cu[N(CN)\({}_{2}\)]Br & 3.64375 \(\times\) 10\({}^{-30}\) & 7 \(\times\) 10\({}^{26}\) & 402 & 11.6 \\ (TMTSF)\({}_{2}\)PF\({}_{6}\) & 3.64375 \(\times\) 10\({}^{-30}\) & 3 \(\times\) 10\({}^{26}\) & 614 & 1.2 \\ CeCoIn\({}_{5}\) & 8.28954 \(\times\) 10\({}^{-30}\) & 5 \(\times\) 10\({}^{25}\) & 2267 & 2.3 \\ CeRhIn\({}_{5}\) & 8.28954 \(\times\) 10\({}^{-30}\) & 2.5 \(\times\) 10\({}^{25}\) & 3206 & 0.4 \\ \hline \end{tabular}
\end{table} 
Table 2: Magnetic field penetration depth in superconductor II. The variability of \(\lambda\) between 40 and 614 nm in type II superconductors reflects differences in the structure and electron density of the materials. Low \(\lambda\) values correspond to superconductors with strong magnetic exclusion and a high carrier density, while high \(\lambda\) values indicate deeper magnetic penetration, typical of materials with lower carrier density or complex structures, allowing the formation of more vortices within the material without breaking the conductivity state.