Question

Electromagnetic waves travel in a medium with a speed of $2\times 10^{8}m/s$ . If the relative permeability of the medium is $1$ the relative permittvity will be

• A. 1.5
• B. 2.25
• C. 3.3
• D. 1.0

Answer 1

Answer: (B)

Given, speed of $EM$ wave $=2\times 10^{8}m/s$-
${\mu }_r=1$
${\epsilon }_r=?$
The velocity or speed of $EM$ wave in the medium,
$v=\frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}\times \frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
We have, $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
where ${\mu }_0$ and ${\epsilon }_0$ are permeability and permittivity of vacuum respectively.
$\therefore v=\frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}\cdot c$
$\frac{2\times 10^8}{3\times 10^8}=\frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}\left[\because C=3\times 10^{8}ms\right]$
$\frac{2}{3}=\frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}$
${\left(\frac{2}{3}\right)}^2=\frac{1}{{\mu }_r{\epsilon }_r}=\frac{1}{1\times {\epsilon }_r}$
Permittivity, ${\epsilon }_r=\frac{9}{4}=2.25$