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

E = 20cos(2 $\times$ 10¹⁰ t $-$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $\mu$_r = 1)

Given, electric field,<br/><br/>E = 20 cos(2 $\times$ 10¹⁰t $-$ 200 x) V/m<br/><br/>Comparing with the standard equation,<br/><br/>E = E₀ cos($\omega$t $-$ kx) V/m, we get<br/><br/>Wave constant, k = 200<br/><br/>Angular frequency, $\omega$ = 2 $\times$ 10¹⁰ rad/s<br/><br/>Speed of the wave, $v = {\omega \over k} = {{2 \times {{10}^{10}}} \over {200}} = {10^8}$ m/s<br/><br/>Refractive index, $\mu = {c \over v} = {{3 \times {{10}^8}} \over {{{10}^8}}} = 3$<br/><br/>As we know the relation between the refractive index and dielectric constant,<br/><br/>$\mu = \sqrt {{\varepsilon _r}{\mu _r}}$<br/><br/>Substituting the value in the above equations, we get<br/><br/>$3 = \sqrt {{\varepsilon _r}(1)}$<br/><br/>${\varepsilon _r} = 9$<br/><br/>Thus, the dielectric constant of the medium is 9.