Question

The electromagnetic waves travel in a medium at a speed of $2.0\times 10^{8}m/s$. The relative permeability of the medium is $1.0$. The relative permittivity of the medium will be:

• A. $2.25$
• B. $4.25$
• C. $6.25$
• D. $8.25$

Answer 1

Answer: (A)

Given,
Speed of electromagnetic waves, $v=2\times 10^{8}m/s$
Relative permeability of the medium $=1$
Speed of light, $C=3\times 10^{8}m/s$
Using the formula of speed of electromagnetic wave in a medium,
$\begin{array}{l}v=\frac{1}{\sqrt{\mu \epsilon }}\\ v=\frac{1}{\sqrt{{\mu }_0{\mu }_r\left({\epsilon }_0{\epsilon }_r\right)}}\\ v=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\times \frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}\end{array}$
Therefore,
Relative permittivity,
$\begin{array}{rl}{\epsilon }_r& =\frac{c^2}{v^2{\mu }_r}\\ & =\frac{{\left(3\times 10^8\right)}^2}{{\left(2\times 10^8\right)}^2\times 1}\\ & =2.25\end{array}$