Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by $E = 20 \cos (2 \times 10^{10} t - 200 x) V m^{- 1} .$ The dielectric constant of the medium is equal to:
(Take $μ_{r} = 1)$

Question

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by

E = 20 \cos (2 \times 10^{10} t - 200 x) V m^{- 1} .

The dielectric constant of the medium is equal to:
(Take

μ_{r} = 1)

Aicharya · Accepted Answer

Equate the wave equation with the equation of EM wave,

E = E_{0} \cos (ω t - k x) V m^{- 1}

here the given equation of EM wave,

E = 20 \cos (2 \times 10^{10} t - 200 x) V m^{- 1}

\Rightarrow v = \frac{ω}{k} = \frac{2 \times 10^{10}}{200} = 10^{8} m s^{- 1}

The refractive index,

\Rightarrow n = \frac{c}{v} = \frac{3 \times 10^{8}}{10^{8}} \Rightarrow 3 = \sqrt{μ_{r} ε_{r}} (μ_{r} = 1 given)

ε_{r} = 9

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = 20…