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 \(=3 \times 10^8 m s ^{-1}\) and for the given medium \(\mu_{ r }=1\) )

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Answer & Solution

Correct Answer

(A) \(5\)

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Detailed explanation

\(V =\frac{ C }{\mu} \Rightarrow \mu=\frac{ C }{ V }=\frac{ C }{0.2 C }\)

\(\mu=5\)

\(\mu=\sqrt{\epsilon_{ r } \mu_{ r }}\)

\(\Rightarrow \epsilon_{ r }=\frac{\mu^2}{\mu_{ r }}\)

\(\therefore \frac{\epsilon_{ r }}{\mu}=\frac{\mu}{\mu_{ r }}=5\)

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