The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, E_ y =20 (3 10⁶ x-4.5 10¹⁴ t ) V / m (where x, t and other values have S.I. units). The dielectric constant of the medium is _ _ _ _ (speed of light in free space is 3 10⁸ ~m / s )

Step-by-step solution

From the wave equation E_y = 20 (3 10^6 x - 4.5 10¹⁴ t) : Wave number: k = 3 10^6 m⁻¹ Angular frequency: = 4.5 10¹⁴ rad/s Speed of wave in medium: v = k = 4.5 10¹⁴ 3 10^6 = 1.5 10^8 m/s Speed of light in vacuum: c = 3 10^8 m/s Refractive index: n = c v = 3 10^8 1.5 10^8 = 2 For a nonmagnetic medium: n = _r Dielectric constant: _r = n^2 = 4