An EM wave from air enters a medium. The electric fields are E₁ = E₀₁îcos [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 nonmagnetic. If ε_r and ε_r' refer to relative permittivities of a

Question

An EM wave from air enters a medium. The electric fields are E₁ = E₀₁îcos [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 nonmagnetic. If ε_r and ε_r' refer to relative permittivities of air and medium respectively, which of the following options is correct?

Accepted Answer

ε_r/ε_r' = 1/4. The ratio of the relative permittivities is determined by the relationship between the wave numbers in different media. Since the wave number in the medium is related to the speed of light and the permittivity, the decrease in wave number indicates an increase in permittivity, leading to the conclusion that the relative permittivity of air is four times that of the medium.

Solution

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