Rotational Motion

JEE Main level, single correct, medium

275 of 280

Question 275 of 280

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E=20cos⁡(2×1010t−200x)Vm−1.E=20\cos \left(2\times {10}^{10}t-200x\right)V{m}^{-1}. The dielectric constant of the medium is equal to:
(Take μr=1){\mu }_{r}=1)

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Answer: (C) 99

Equate the wave equation with the equation of EM wave, E=E0cos⁡(ωt−kx)Vm−1E={E}_{0}\cos \left(\omega t-kx\right)V{m}^{-1} here the given equation of EM wave, E=20cos⁡(2×1010t−200x)Vm−1E=20\cos \left(2\times {10}^{10}t-200x\right)V{m}^{-1}⇒v=ωk=2×1010200=108ms−1\Rightarrow v=\dfrac{\omega }{k}=\dfrac{2\times {10}^{10}}{200}={10}^{8}m{s}^{-1}
The refractive index,⇒n=cv=3×108108⇒3=μrϵr(μr=1given)\Rightarrow n=\dfrac{c}{v}=\dfrac{3\times {10}^{8}}{{10}^{8}} \Rightarrow 3=\sqrt{{\mu }_{r}{\epsilon }_{r}}\left({\mu }_{r}=1\right.\text{given})
ϵr=9{\epsilon }_{r}=9

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