Answer:
0.80267 m
Explanation:
E(z) = Electric field = 1 µV/m
[tex]E_0[/tex] = 20 V/m
z = Depth
[tex]\sigma[/tex] = Conductivity = 0.1 S/m
[tex]\epsilon_r[/tex] = 81
[tex]\mu[/tex] = Impedance of free space = [tex]120\pi\ \Omega[/tex]
Frequency is given by
[tex]E(z)=E_0e^{-\alpha z}[/tex]
Parameter is given by
[tex]\alpha=\dfrac{\sigma}{2}\sqrt{\dfrac{\mu}{\epsilon_r}}\\\Rightarrow \alpha=\dfrac{1}{2}\sqrt{\dfrac{(120\pi)^2}{81}}\\\Rightarrow \alpha=20.94395\ N_p/m[/tex]
From the first equation
[tex]1\times 10^{-6}=20e^{-20.94395z}\\\Rightarrow ln\dfrac{1\times 10^{-6}}{20}=-20.94395z\\\Rightarrow z=\dfrac{ln\dfrac{1\times 10^{-6}}{20}}{-20.94395}\\\Rightarrow z=0.80267\ m[/tex]
The depth is 0.80267 m
