Physics - EM Waves Question with Solution | TestHub

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

The speed of electromagnetic waves in a medium is given by

$\text{v}=\frac{1}{\sqrt{\text{μ}\text{ε}}}\text{,}\text{....(i)}$

where$\mu$and$\epsilon$are absolute permeability and absolute permittivity of the medium.

Now,$\mu ={\mu }_0{\mu }_r$and$\epsilon ={\epsilon }_0{\epsilon }_r$

Therefore, the equation (i) becomes

$\text{v}=\frac{1}{\sqrt{{\text{μ}}_0{\text{μ}}_{\text{r}}\times {\text{ε}}_0{\text{ε}}_{\text{r}}}}=\frac{1}{\sqrt{{\text{μ}}_0{\text{ε}}_{\text{0}}}}\times \frac{1}{\sqrt{{\text{μ}}_{\text{r}}{\text{ε}}_{\text{r}}}}=\frac{\text{c}}{\sqrt{{\text{μ}}_{\text{r}}{\text{ε}}_{\text{r}}}}$

$\text{or}{\text{ε}}_{\text{r}}=\frac{{\text{c}}^2}{{\text{v}}^2{\text{μ}}_{\text{r}}}=\frac{{\left(3\times {\text{10}}^8\right)}^2}{{\left(2\times {\text{10}}^8\right)}^2\times 1}=\text{2.25}$