Q141 / 180 · COMEDK 2015 · Physics
The refractive index and the permeability of a medium are respectively $1.5$ and $5 \times 10^{-7} \mathrm{Hm}^{-1}$. The relative permittivity of the medium is nearly
- A$25$
- B$15$
- Correct answerC$6$
- D$10$
Solution
Given, refractive index of the medium, $n=15$
Permeability of the medium,
$$
\mu=5 \times 10^{-7} \mathrm{Hm}^{-1}
$$
Relative permeability of the medium,
$$
\mu_{r}=\frac{\mu}{\mu_{0}}=\frac{5 \times 10^{-7}}{4 \pi \times 10^{-7}}=\frac{5}{4 \pi}
$$
We know that, refractive index,
$$
\begin{aligned}
n &=\sqrt{\varepsilon_{r} \mu_{r}} \\
n^{2} &=\varepsilon_{r} \mu_{r} \\
\Rightarrow \quad \varepsilon_{r} &=\frac{n^{2}}{\mu_{r}}=\frac{(1.5)^{2}}{5 / 4 \pi} \\
&=\frac{(1.5)^{2} \times 4 \pi}{5}=5.7 \simeq 6
\end{aligned}
$$
Hence, the correct answer is option: 'C'.