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JEE Main 2023 (31 Jan, Shift 1) · Speed of EM Waves in a Medium

Speed of EM Waves in a Medium question from JEE Main 2023 (31 Jan, Shift 1)

Q9JEE Main 2023 · 31 JAN · SHIFT 1Medium

Speed of EM Waves in a Medium

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x : 1$ . The value of $x$ is _________. (Given speed of light in free space $= 3 \times 10^{8}\text{ m s}^{-1}$ and for the given medium $\mu_r = 1$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 5

$v = 0.2c \Rightarrow n = c/v = 5$
With $\mu_r = 1$ : $n = \sqrt{\varepsilon_r} \Rightarrow \varepsilon_r = n^2 = 25$
$\dfrac{\varepsilon_r}{n} = \dfrac{25}{5} = 5$
So $x = 5$ .

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