Question

A plane wave propagating through a medium $[{ϵ}_r=8,{\mu }_r=2,and\sigma =0]$ has its electric field given by

$\overrightarrow{E}=0.5sin({10}^{8}t-\beta z)V/m$ The wave impedance, in ohms is

• A. $198.5\angle {180}^{\circ }$
• B. 377
• C. $182.9\angle {14}^{\circ }$
• D. 188.5

Answer 1

The correct option is D 188.5

Ans : (d)

$\eta =\sqrt{\frac{j\omega \mu }{\sigma +j\omega ϵ}},\sigma =0$

$\sqrt{\frac{\mu }{ϵ}}\angle 0^{\circ }$

$=\sqrt{\frac{{\mu }_0{\mu }_r}{{ϵ}_0{ϵ}_r}}=\sqrt{\frac{{\mu }_0}{{ϵ}_0}}\sqrt{\frac{{\mu }_r}{{ϵ}_r}}$

$=377\sqrt{\frac{2}{8}}=\frac{377}{2}=188.5$