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

Question

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

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

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

{\mu}_{r} = 1 )

Quantrex Academy · Accepted Answer

Correct answer: C. 9

Equate the wave equation with the equation of EM wave,

E = {E}_{0}\cos \left(\omegat - kx\right)V{m}^{- 1}

here the given equation of EM wave,

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

⇒ v = \dfrac{\omega}{k} = \dfrac{2 \times {10}^{10}}{200} = {10}^{8}m{s}^{- 1}

The refractive index,

⇒ n = \dfrac{c}{v} = \dfrac{3 \times {10}^{8}}{{10}^{8}} ⇒ 3 = \sqrt{{\mu}_{r}{ε}_{r}}\left({\mu}_{r} = 1\right\text{given} )

{ε}_{r} = 9

Electric field of a plane electromagnetic wave propagating through...