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JEE Main 20254 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2025 · 4 April · Evening Shift · Physics · Electromagnetic Waves

If an optical medium possesses a relative permeability of (10)/(π)...

If an optical medium possesses a relative permeability of 10π\frac{10}{\pi} and relative permittivity of 10.0885\frac{1}{0.0885}, then the velocity of light is greater in vacuum than that in this medium by ________ times.
(μ0=4π×10−7H/m,ϵ0=8.85×10−12 F/m\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.
c=3×108 m/s)\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)

Correct answer

0

Step-by-step solution

Since velocity of light in terms of μ&E\mu \& E is
<br/>V=1μϵ=1μ0μr×1ϵ0ϵr=1μrϵr×1μ0ϵ0=Cμrϵr=C10π×10.0885=C36=C6<br/>\begin{aligned}<br/>& V=\frac{1}{\sqrt{\mu \epsilon}}=\frac{1}{\sqrt{\mu_0 \mu_r}} \times \frac{1}{\sqrt{\epsilon_0 \epsilon_r}} \\ & =\frac{1}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}} \times \frac{1}{\sqrt{\mu_0 \epsilon_0}} \\ & =\frac{C}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\frac{10}{\pi} \times \frac{1}{0.0885}}} \\ & =\frac{C}{\sqrt{36}}=\frac{C}{6}<br/>\end{aligned}
<br/>V=C6C=6 V<br/>\begin{aligned}<br/>\mathrm{V} & =\frac{\mathrm{C}}{6} \\ \mathrm{C} & =6 \mathrm{~V}<br/>\end{aligned}
Velocity of light in vacuum is greater by 6 times the velocity of light in medium
Answer is 6
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