Electromagnetic Waves

JEE Main level, numerical answer, medium

88 of 165

Question 88 of 165

An electromagnetic wave of frequency 3GHz3GHz enters a dielectric medium of relative electric permittivity 2.252.25 from vacuum. The wavelength of this wave in that medium will be _________ ×10−2cm.\times {10}^{-2}cm.

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Answer: 667

λ\lambda in vacuum =cf=3×1083×109=0.1m=\dfrac{c}{f}=\dfrac{3\times {10}^{8}}{3\times {10}^{9}}=0.1m
∴λ∴\lambda in medium =0.1μ=\dfrac{0.1}{\mu }
Where refractive index
μ=μrϵr\mu =\sqrt{{\mu }_{r}{\epsilon }_{r}}
Assuming non-magnetic material μr=1{\mu }_{r}=1
∴μ=2.25=1.5∴\mu =\sqrt{2.25}=1.5
λm=0.11.5=115m=6.67cm{\lambda }_{m}=\dfrac{0.1}{1.5}=\dfrac{1}{15}m=6.67cm
=667×10−2cm=667\times {10}^{-2}cm

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