## 3 The Electric Fields in the Medium
### Attenuation in Various Types of Water  
In this chapter, the value of the loss tangent is calculated according to the type of water in the band below 15 MHz, where the CPT system is mainly used. Table 1 shows the conductivity of each type of water under the same conditions. Each type of water has a different conductivity at 25 \({}^{\circ}\)C, but has the same relative permittivity of 81.  
Figure 6 shows the loss tangent values in the frequency range from 0.1 MHz to 15 MHz. The loss tangent was calculated for four types of water, and their conductivities and relative permittivities are shown in Table 3. As shown in Figure 6, the loss tangent of distilled water is much less than 1 in all frequency bands in which the CPT system operated and can be evaluated as good dielectric material. The loss tangent of tap water and river water, in which some electrolytes are dissolved, can have both conductive and dielectric properties depending on the operating frequency. According to Figure 6, tap water can be considered as a dielectric material above a frequency of about 5 MHz, and river water can be considered as a dielectric material above a frequency of about 8 MHz. However, even if both media are considered as dielectric materials, it is clear that they have high losses in the MHz band. Since dielectrics are generally defined as tan\(\delta<0.01\), both mediums are included in the category of conductors unless they are used at higher frequencies. Unlike the previous three types of water, the loss tangent of seawater greatly exceeds 1 in all frequency bands in  
which the CPT system operated and can be evaluated as a good conductor. This indicates that electromagnetic fields propagating in seawater media cause much larger conduction losses than other types of water. As can be seen in Equation (9a) in the previous section, the strength of the electric field within the medium exponentially decreases according to the propagation distance due to the attenuation constant \(\alpha\), which is the real part of the propagation constant \(\hat{\gamma}\).  
Figure 7 shows the attenuation of the electric field for various types of water medium according to the propagation distance from 0 to 300 mm. The intensity of the four medium electric fields is 1 V/m at 0 mm and decreases with distance. As can be seen in Figure 7, distilled water has no attenuation of the electric field up to the medium gap. However, for tap water and river water, there is a gradual attenuation as the distance increases. As a result, the electric fields of tap water and river water decreased to 0.9 V/m and 0.8 V/m, respectively, at 300 mm. Unlike other types of water, sea water shows a significant decrease in the electric field of about 0.6 V/m at 50 mm and 0.05 V/m at 300 mm depending on the propagation distance. This proves that sea water acts as a conductor rather than a dielectric in the CPT system and that it must also have a short transfer distance in the MHz band. In conclusion, distilled water is evaluated as a dielectric and can have a positive effect on improving the performance of the CPT system. According to Figures 1 and 2, tap water and river water belong to the category of conductors, but they can be limitedly used in the CPT system as long as there is a short medium gap. On the other hand, sea water can be evaluated as a conductor due to its high conductivity and cannot be properly used in a CPT system due to the huge electric field attenuation effect even in a short medium gap.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Water** & **Conductivity** & **Relative Permittivity** \\ \hline Distilled water & 0.0002 [S/m] & 81 \\ Tap water & 0.02 [S/m] & 81 \\ River water & 0.04 [S/m] & 81 \\ Sea water & 4 [S/m] & 81 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Conductivity and permittivity of various types of water at 25 \({}^{\circ}\)C [19].  
Figure 6: The loss tangent values for various types of water from 0.1 to 15 MHz.