Light In Conductors

#Physics

$\displaystyle \tilde{E}(z,t)=\tilde{E}_{0}e^{i(\tilde{k}z-\omega t)}$

• Electric field inside conductors

$\displaystyle \tilde{B}(z,t)=\tilde{B}_{0}e^{i(\tilde{k}z-\omega t)}$

$\displaystyle \tilde{k}=k+i\kappa$

$\displaystyle k\equiv \omega\sqrt{ \frac{\varepsilon \mu}{2} }\sqrt{ \sqrt{ 1+\left( \frac{\sigma}{\varepsilon \omega} \right)^{2} } +1 }$

• $\displaystyle \varepsilon$ is the permittivity of the material
• $\displaystyle \mu$ is the permeability of the material

$\displaystyle \kappa\equiv \omega\sqrt{ \frac{\varepsilon \mu}{2} }\sqrt{ \sqrt{ 1+\left( \frac{\sigma}{\varepsilon \omega} \right)^{2} }-1 }$

$\displaystyle d=\frac{1}{\kappa}$

• Skin depth of a material. The distance it takes for the amplitude of a wave to decrease by a factor of $\displaystyle \frac{1}{e}$