Question

A plane wave propagating in air with $\overrightarrow{E}=(8\widehat{a_x}+6\widehat{a_y}+5\widehat{a_z})$ $e^{j(\omega t+3x-4y)}$ V/m is incident on a perfectly conducting slab positioned at $x\le 0$. the $\overrightarrow{E}$ field of the reflected waves is

• A. $(-8{\hat{a}}_x+6{\hat{a}}_y-5{\hat{a}}_z)e^{j(\omega t+3x+4y)}V/m$
• B. $(8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z)e^{j(\omega t-3x-4y)}V/m$
• C. $(-8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z)e^{j(\omega t+3x+4y)}V/m$
• D. $(8{\hat{a}}_x+6{\hat{a}}_y-5{\hat{a}}_z)e^{j(\omega t-3x-4y)}V/m$

Answer 1

The correct option is B $(8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z)e^{j(\omega t-3x-4y)}V/m$

Ans : (c)

Incident wave propagation $\to -3{\hat{a}}_x+4{\hat{a}}_y$

Reflected wave propagation $\to 3{\hat{a}}_x+4{\hat{a}}_y$

$E_i$ incident direction $\to 8{\hat{a}}_x+6{\hat{a}}_y+5{\hat{a}}_z$

$\begin{array}{c}{E}_{i}tangential\to 6{\hat{a}}_y+5{\hat{a}}_z\\ E_{r}tangential\to 6{\hat{a}}_y-5{\hat{a}}_z\end{array}\}{E}_{tang}=0$

$\begin{array}{c}{E}_{i}normal=8{\hat{a}}_x\\ E_{r}normal=8{\hat{a}}_x\end{array}\}{E}_{normal}=E_{max}$

$E_{r}reflecteddirection=8{\hat{a}}_x-6{\hat{a}}_y-5{\hat{a}}_z$