Q137 / 180 · COMEDK 2022 · Physics
Speed of electromagnetic wave in a medium having relative permittivity $\varepsilon_r$ and relative permeability $\mu_r$ is (speed of light in air, $\left.c=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$
- A$\dfrac{1}{\sqrt{\mu_r \varepsilon_r}}$
- Correct answerB$\dfrac{c}{\sqrt{\mu_r \varepsilon_r}}$
- C$c \sqrt{\dfrac{\mu_r}{\varepsilon_r}}$
- D$\dfrac{c}{\mu_r \varepsilon_r}$
Solution
The speed of an electromagnetic wave in a vacuum is given by $c = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}$.
The speed of an electromagnetic wave in a medium with absolute permittivity $\varepsilon$ and absolute permeability $\mu$ is given by $v = \dfrac{1}{\sqrt{\mu \varepsilon}}$.
The absolute permittivity and permeability are related to their relative values by $\varepsilon = \varepsilon_0 \varepsilon_r$ and $\mu = \mu_0 \mu_r$.
Substituting these into the expression for $v$, we get $v = \dfrac{1}{\sqrt{(\mu_0 \mu_r)(\varepsilon_0 \varepsilon_r)}} = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0} \sqrt{\mu_r \varepsilon_r}}$.
Since $c = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}$, the expression becomes $v = \dfrac{c}{\sqrt{\mu_r \varepsilon_r}}$.
Answer: $\dfrac{c}{\sqrt{\mu_r \varepsilon_r}}$
The speed of an electromagnetic wave in a medium with absolute permittivity $\varepsilon$ and absolute permeability $\mu$ is given by $v = \dfrac{1}{\sqrt{\mu \varepsilon}}$.
The absolute permittivity and permeability are related to their relative values by $\varepsilon = \varepsilon_0 \varepsilon_r$ and $\mu = \mu_0 \mu_r$.
Substituting these into the expression for $v$, we get $v = \dfrac{1}{\sqrt{(\mu_0 \mu_r)(\varepsilon_0 \varepsilon_r)}} = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0} \sqrt{\mu_r \varepsilon_r}}$.
Since $c = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}$, the expression becomes $v = \dfrac{c}{\sqrt{\mu_r \varepsilon_r}}$.
Answer: $\dfrac{c}{\sqrt{\mu_r \varepsilon_r}}$
Hence, the correct answer is option: 'B'.