Question

Electromagnetic waves travelling in a medium which has relative permittivity $1.3$ and relative permeability $2.14$ speed of electromagnetic waves in this medium will be _________

• A. $3.6\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• B. $1.8\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• C. $1.8\times {10}^6\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$
• D. $13.6\times {10}^6\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Answer 1

The correct option is B

$1.8\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step 1. Given data

The relative permittivity of the electromagnetic wave is ${\epsilon }_0=1.3$

The relative permeability of electromagnetic waves is ${\mu }_0=2.14$

Step 2. Calculation of speed of the electromagnetic wave.

The speed of electromagnetic waves is given by $v=\frac{c}{{\epsilon }_r{\mu }_r}$

Where $V$ is the speed of the electromagnetic wave

$c$is the velocity of light $\left(c=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.\right)$

${\epsilon }_0$ is the relative permittivity of electromagnetic wave

${\mu }_0$ is the relative permeability of electromagnetic wave

By substituting the values in the above formula, we get

$$\begin{gathered} V=\frac{3\times {10}^8}{1.3\times 2.14} \\ =1.79\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \\ \cong 1.8\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \end{gathered}$$

Hence, the correct option is (B)