Question

The magnetic field component of an electromagetic wave propagating through a non-magnetic medium is given by $\overrightarrow{H}=6cos(2\times {10}^{8}t-6x)\hat{j}A{m}^{-1}$ where$x,t$ are in $SI$ units . The relative permittivity of the medium is

• A. $6$
• B. $36$
• C. $9$
• D. $81$

Answer 1

The correct option is D $81$

For non-magnetic medium, Permeability = ${\mu }_0|\because {\mu }_r=1|$

From the given equation, $\omega =2\times {10}^{8}rad/s$
$k=6$
Speed of Electromagnetic wave in non magnetic medium is
$v=\frac{1}{\sqrt{{\mu }_0{ϵ}_0.{ϵ}_r}}=\frac{\omega }{k}$
$\Rightarrow \frac{1}{\sqrt{{\mu }_0{ϵ}_0.{ϵ}_r}}=\frac{2\times {10}^8}{6}$

$\because$ speed of Electromagnetic wave in vacuum is
$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

$\Rightarrow \frac{3\times {10}^8}{\sqrt{{ϵ}_r}}=\frac{2\times {10}^8}{6}$
$\Rightarrow \sqrt{{ϵ}_r}=\frac{6\times 3}{2}=9$

$\therefore {ϵ}_r=9^2\Rightarrow 81$