Question

A plane wave having the electric field component $\overrightarrow{E_i}=24cos(3\times {10}^{8}t-\beta y)\widehat{a_z}$ V/m and traveling in free space is incident normally on a lossless medium with $\mu ={\mu }_0$ and $ϵ=9{ϵ}_0$ which occupies the region $y\ge 0$. The reflected magnetic field component is given by

Answer 1

Ans : (a)

$\overrightarrow{E_i}=24cos(3\times {10}^{8}t-\beta y){\hat{a}}_{z}V/m$

The wave is travelling in +y direction.

$H_i=\frac{1}{\eta }({\hat{a}}_y\times {\overrightarrow{E}}_i)$

$=\frac{24cos}{120\pi }(3\times {10}^{8}t-\beta y){\hat{a}}_x$

$=\frac{1}{5\pi }cos(3\times {10}^{8}t-\beta y){\hat{a}}_x$

$\frac{H_r}{H_i}=\frac{{\eta }_1-{\eta }_2}{{\eta }_1+{\eta }_2}=\frac{\sqrt{\frac{{\mu }_0}{{ϵ}_1}}-\sqrt{\frac{{\mu }_0}{{ϵ}_2}}}{\sqrt{\frac{{\mu }_0}{{ϵ}_1}}+\sqrt{\frac{{\mu }_0}{{ϵ}_2}}}$

= $\frac{\sqrt{{ϵ}_2}-\sqrt{{ϵ}_1}}{\sqrt{{ϵ}_2}+\sqrt{{ϵ}_1}}=\frac{\sqrt{9}-\sqrt{1}}{\sqrt{9}+\sqrt{1}}=\frac{3-1}{3+1}=\frac{2}{4}=\frac{1}{2}$

Therfore, reflected magnetic field component,

${\overrightarrow{H}}_r=\frac{1}{10\pi }cos(3\times {10}^{8}t+\beta y){\hat{a}}_x$

Due to change in propagation direction to -y