Physics - EM Waves Question with Solution | TestHub

Here,$v=2\times {10}^8\text{m}{\text{s}}^{-1}$and${\mu }_{\mathrm{r}}=1$

The speed of electromagnetic waves in a medium is given by$v=\frac{1}{\sqrt{\mu \epsilon }} ...\left(i\right)$

where$\mu$and$\epsilon$are absolute permeability and absolute permittivity of the medium.
Now,$\mu ={\mu }_0{\mu }_{\mathrm{r}}$and$\epsilon ={\epsilon }_0{\epsilon }_{\mathrm{r}}$
Then, we have,

$v=\frac{1}{\sqrt{{\mu }_0{\mu }_{\mathrm{r}}\times {\epsilon }_0{\epsilon }_{\mathrm{r}}}}=\frac{1}{\sqrt{{\mu }_0{\epsilon }_{\mathrm{0}}}}\times \frac{1}{\sqrt{{\mu }_{\mathrm{r}}{\epsilon }_{\mathrm{r}}}}=\frac{c}{\sqrt{{\mu }_{\mathrm{r}}{\epsilon }_{\mathrm{r}}}}$

$or{\epsilon }_{\mathrm{r}}=\frac{c^2}{v^2{\mu }_r}=\frac{{\left(3\times {\mathrm{10}}^8\right)}^2}{{\left(2\times {\mathrm{10}}^8\right)}^2}=\frac{9}{4}=2.25$