Q 12-08-236JEE MainJEE Main 2025 (4 Apr, Shift 2)Easy
If an optical medium possesses a relative permeability of $\dfrac{10}{\pi}$ and relative permittivity of $\dfrac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by ______ times. ($\mu_0 = 4\pi\times10^{-7}\ \text{H/m}$, $\varepsilon_0 = 8.85\times10^{-12}\ \text{F/m}$, $c = 3\times10^8\ \text{m/s}$)
Numerical value type. Enter your answer.
Answer: 6
$v = \dfrac{1}{\sqrt{\mu\varepsilon}} = \dfrac{c}{\sqrt{\mu_r\varepsilon_r}}$, so
$$\frac cv = \sqrt{\mu_r\varepsilon_r} = \sqrt{\frac{10}{\pi}\times\frac{1}{0.0885}} = \sqrt{\frac{10}{0.278}} \approx \sqrt{36} = 6$$
Solution by Sreeraj P, M.Sc Physics