Electromagnetic Waves

JEE Main level, numerical answer, medium

90 of 165

Question 90 of 165

An electromagnetic wave of frequency 5GHz5GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2.2. Its velocity in this medium is _______×107ms−1\times {10}^{7}m{s}^{-1}.

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Answer: 15

Given : Frequency of wave f=5GHzf=5GHz
=5×109Hz=5\times {10}^{9}Hz
Relative permittivity, ϵr=2{ϵ}_{r}=2 and Relative permeability, μr=2{\mu }_{r}=2 Since speed of light in a medium is given by,
v=1μ∈=1μrμ0⋅ϵr∈0v=\dfrac{1}{\sqrt{\mu }\in }=\dfrac{1}{\sqrt{{\mu }_{r}{\mu }_{0}\cdot {ϵ}_{r}{\in }_{0}}}
v=1μrϵf1μ0ϵ0=Cμrϵrv=\dfrac{1}{\sqrt{{\mu }_{r}{ϵ}_{f}}}\dfrac{1}{\sqrt{{\mu }_{0}{ϵ}_{0}}}=\dfrac{C}{\sqrt{{\mu }_{r}{ϵ}_{r}}}
Where CC is speed of light is vacuum
∴v=3×1084=30×1072ms−1∴v=\dfrac{3\times {10}^{8}}{\sqrt{4}}=\dfrac{30\times {10}^{7}}{2}m{s}^{-1}
=15×107ms−1=15\times {10}^{7}m{s}^{-1}
∴∴ Ans. is 1515

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