Question

An electromagnetic wave of frequency $3GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be $......\times 10^{-2}cm$ .

Answer 1

Answer: 667

$f=3GHz,{ϵ}_r=2.25$
$v=\lambda f\Rightarrow \lambda =\frac{v}{f}$
$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
$v=\frac{1}{\sqrt{{\mu }_0{\mu }_r{ϵ}_0{ϵ}_r}}\Rightarrow \lambda =\frac{1}{f\cdot \sqrt{{\mu }_0{ϵ}_0}\cdot \sqrt{{\mu }_r{ϵ}_r}}$
$\Rightarrow \lambda =\frac{C}{f\cdot \sqrt{{\mu }_r}\cdot \sqrt{{ϵ}_r}}\Rightarrow \lambda =\frac{3\times 10^8}{3\times 10^9\times \sqrt{1}\times \sqrt{2.25}}$
$\Rightarrow \lambda =667\times 10^{-2}cm$