Electromagnetic Waves

JEE Main level, single correct, medium

12 of 165

Question 12 of 165

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3k=3 and permeability of μ=2μ0\mu=2 \mu_{0}, is
(μ0=\mu_{0}= permeability of vacuum)

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Answer: (D) 6:1\sqrt{6}: 1

Speed of electromagnetic wave in vacuum: c=1μ0ϵ0c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}
Speed in a medium with permeability μ=2μ0\mu = 2\mu_0 and dielectric constant k=3k = 3:
v=1μϵ=12μ0×3ϵ0=16μ0ϵ0v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{1}{\sqrt{2\mu_0 \times 3\epsilon_0}} = \frac{1}{\sqrt{6\mu_0\epsilon_0}}
v=16×1μ0ϵ0=c6v = \frac{1}{\sqrt{6}} \times \frac{1}{\sqrt{\mu_0\epsilon_0}} = \frac{c}{\sqrt{6}}
Ratio of speeds: cv=6\frac{c}{v} = \sqrt{6}
Therefore: c:v=6:1c : v = \sqrt{6} : 1

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