The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,

$$ E_{y}=20 \sin (3\times 10^{6}x - 4.5\times 10^{14}t)V/m $$
(where $$x, t$$ and other values have S.I. units). The dielectric constant of the medium iS_________
(speed oflight in free space is $$ 3\times 10^{8} m/s $$)

The electric field of a plane EM wave in a non-magnetic medium is $$E_y = 20\sin(3 \times 10^6 x - 4.5 \times 10^{14} t)$$ V/m. Find the dielectric constant.

The wave number is $$k = 3 \times 10^6$$ rad/m and the angular frequency is $$\omega = 4.5 \times 10^{14}$$ rad/s.

The phase velocity in the medium is $$v = \frac{\omega}{k} = \frac{4.5 \times 10^{14}}{3 \times 10^6} = 1.5 \times 10^8$$ m/s.

The refractive index is $$n = \frac{c}{v} = \frac{3 \times 10^8}{1.5 \times 10^8} = 2$$.

For a non-magnetic medium ($$\mu_r = 1$$), we have $$n = \sqrt{\epsilon_r}$$, so $$\epsilon_r = n^2 = 4$$.

The answer is 4.