Question

Consider a uniform plane wave with amplitude $\left(E_0\right)$ of 10 V/m and 1.1 GHz frequency travelling an air, and incident normally on a dielectric medium with complex relative permittivity $\left({ϵ}_r\right)$ and permeability $\left({\mu }_r\right)$ as shown in the figure.







The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm inside the dielectric region is ________

Answer 1

Material has ${\mu }_R$ and ${ϵ}_R$ complex,

$\eta$ of material = $\sqrt{\frac{j\omega \mu }{\sigma +j\omega ϵ}}=\sqrt{\frac{{\mu }_0{\mu }_R}{{ϵ}_0{ϵ}_R}}=120\pi$

where, $\sigma =0$ (dielectric)

No reflactions at the boundary.

$\gamma =$ Propagation constant

$=\sqrt{j\omega {\mu }_0{\mu }_R(0+j\omega {ϵ}_0{ϵ}_R)}$

$=j\omega \sqrt{{\mu }_0{ϵ}_0}\cdot \sqrt{(1-j2{)}^2}$

$j\omega \sqrt{{\mu }_0{ϵ}_0}+2\omega \sqrt{{\mu }_0{ϵ}_0}$

$\alpha =2\omega \sqrt{{\mu }_0{ϵ}_0}=46.07Np/m$

Magnitude of transmitted electric field component

$\left|E\right|=E_0{e}^{-az}withZ=0.1m$

$\left|E\right|=0.1V/m$