Question

The electric field component of an electromagnetic wave propagating in a lossless medium $1({\mu }_{r1}=1,{\in }_{r1}=4)$ has peak amplitude of 50 V/m. If this wave is normally incident onto a lossless medium $2({\mu }_{r2}=1,{\in }_{r2}=9)$, then the ratio of average transmitted and incident power densities is given by_________.

Answer 1

$\frac{P_i}{P_t}=\frac{1}{(1-|\Gamma {|}^2)}$

Where, $\Gamma =\frac{{\eta }_2-{\eta }_1}{{\eta }_2+{\eta }_1}=\frac{\frac{120\pi }{3}-\frac{120\pi }{2}}{\frac{120\pi }{3}+\frac{120\pi }{2}}=-\frac{1}{5}$

$\therefore \frac{P_i}{P_t}=\left(\frac{1}{1-\frac{1}{25}}\right)\Rightarrow \frac{P_t}{P_i}=0.96$