Given equation of wave \\\\(\\vec{E} = \\vec{E}_0 (4 \ imes \\vec{10} x - 50 t)\\\\)Comparing with general equation of wave,\\\\(\\vec{E} = \\vec{E}_0 (kx - wt),\\\\)we get,\\\\(w = 50\\ rad/s.\\\\) \\\\(k = 4 \ imes 10^{-7} m^{-1}\\\\)Thus velocity of wave, \\\\(v = \\dfrac{w}{k} = \\dfrac{50}{4 \ imes 10^{-7}} = 1.25 \ imes 10^8 m/s\\\\)so, refractive index of medium,\\\\(\\mu = \\dfrac{e}{v} = \\dfrac{3 \ imes 10^8}{1.25 \ imes 10^8} = 2.4\\\\)using, \\\\(u^2 = km.ke\\\\) [km and ke are magnetic and dielectric di - constants]as medium is non diamagnetic, \\\\(km = 1\\\\)\\\\(\\Rightarrow ke = \\mu^2 = (2.4)^2 \\Rightarrow ke = 5.76\\\\)