Question

The electric field intensity of uniform plane wave travelling in a non-magnetic medium is given by $\overline{E}=5\cos (\pi \times {10}^{8}t-\pi z){\hat{a}}_{x}V/m$. The value of dielectric constant of the medium is _____

Answer 1

$Given\overline{E}=5\cos (\pi \times {10}^{8}t-\pi z){\hat{a}}_z$
$\omega =\pi \times {10}^{8}rad/sec$
$\beta =\pi rad/m$
$\text{Medium : non-magnetic,}\mu ={\mu }_o$
$\beta =\omega \sqrt{{\mu }_0{ϵ}_0{ϵ}_r}$
$\beta =\frac{\omega }{v_o}\times \sqrt{{ϵ}_r}$
$\pi =\frac{\pi \times {10}^8}{3\times {10}^8}\sqrt{{ϵ}_r}$
$\sqrt{{ϵ}_r}=3$
$\therefore \text{dielectric constant},{ϵ}_t=9$