Electromagnetic Waves

JEE Main level, single correct, medium

119 of 165

Question 119 of 165

An EM wave from air enters a medium. The electric fields are E⃗1=E01x^cos⁡⁡[2πv(zc−t)]{\vec{E}}_{1}={E}_{01}\hat{x}\cos ⁡\left[2\pi v\left(\dfrac{z}{c}-t\right)\right] in air and E⃗2=E02x^cos⁡⁡[k(2z−ct)]{\vec{E}}_{2}={E}_{02}\hat{x}\cos ⁡\left[k\left(2z-ct\right)\right]in medium, where the wave number k and frequency vv refer to their values in the air. The medium is non-magnetic. If ϵr1{ϵ}_{{r}_{1}} and ϵr2{ϵ}_{{r}_{2}} refer to relative permittivities of air and medium respectively, which of the following options, is correct?

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Answer: (D) ϵr1ϵr2=14\dfrac{{ϵ}_{{r}_{1}}}{{ϵ}_{{r}_{2}}}=\dfrac{1}{4}

∨air∨med=cc/2=2=μ0ϵ0μr2ϵr2μ0ϵ0μr1ϵr1\dfrac{{∨}_{air}}{{∨}_{med}}=\dfrac{c}{c/2}=2=\dfrac{\sqrt{{\mu }_{0}{ϵ}_{0}{\mu }_{{r}_{2}}{ϵ}_{{r}_{2}}}}{\sqrt{{\mu }_{0}{ϵ}_{0}{\mu }_{{r}_{1}}{ϵ}_{{r}_{1}}}}ϵr1ϵr2=14\dfrac{{ϵ}_{{r}_{1}}}{{ϵ}_{{r}_{2}}}=\dfrac{1}{4}

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