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An EM wave from air enters a medium. The electric fields are E₁ = E₀₁x̂cos [2πν ((z)/(c)-t) ] in air and E₂ = E₀₂x̂cos[k(2z-ct)] in medium, where the wave number k and frequency ν refer to their values in air. The medium is non-magnetic. If ε_(r1) and ε_(r2) refer to relative permittivities of air and medium respectively, which of the following options is correct?

1. (ε_(r1))/(ε_(r2)) = 4
2. (ε_(r1))/(ε_(r2)) = 2
3. (ε_(r1))/(ε_(r2)) = (1)/(4)
4. (ε_(r1))/(ε_(r2)) = (1)/(2)

Correct answer: (ε_(r1))/(ε_(r2)) = (1)/(4)

Solution

The correct option indicates that the relative permittivity of the medium is four times that of air, which is consistent with the relationship between wave speed, frequency, and permittivity in different media. Since the wave number in the medium is modified by the permittivity, this ratio reflects how the electric field's behavior changes as it transitions from air to the medium.

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