Question

The speed of electromagnetic wave in a medium whose dielectric constant is $2.25$ and relative permeability is $4$, is equal to

• A. $0.5\times {10}^8\text{m/s}$
• B. $0.25\times {10}^8\text{m/s}$
• C. $0.75\times {10}^8\text{m/s}$
• D. $1\times {10}^8\text{m/s}$

Answer 1

The correct option is D $1\times {10}^8\text{m/s}$

Given:
Dielectric constant $k=2.25$

Relative permeability ${\mu }_r=4$

We know that relative permittivity ${\epsilon }_r$ is equal to the dielectric constant $k$

$\Rightarrow {\epsilon }_r=k=2.25$

Therefore, the speed of electromagnetic wave is given by,

$v=\frac{1}{\sqrt{{\epsilon }_0{\epsilon }_r{\mu }_0{\mu }_r}}$

$=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}\times \frac{1}{\sqrt{{\mu }_r{\epsilon }_r}}v=\frac{c}{\sqrt{{\mu }_r{E}_r}}$

$=\frac{3\times {10}^8}{\sqrt{2.25\times 4}}={10}^8\text{m/s}$

Hence, option $\left(D\right)$ is correct.