A plane electromagnetic wave in a non-magnetic dielectric medium is given by \(\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)\) with distance being in meter and time in seconds. The dielectric constant of the medium is

\(\vec{E}=\vec{E}_{0}(4 \times \overrightarrow{10} x-50 t)\)

Comparing with general equation of wave,

\(\vec{E}=\vec{E}_{0}(k x-w t)\)

we get,

\(w=50\) rad \(/ s . k=4 \times 10^{-7} m^{-1}\)

Thus velocity of wave,

\(v=\frac{w}{k}=\frac{50}{4 \times 10^{-7}}=1.25 \times 10^{8} \mathrm{m} / \mathrm{s}\)

so, refractive index of medium,

\(\mu=\frac{e}{v}=\frac{3 \times 10^{8}}{1.25 \times 10^{8}}=2.4\)

using, \(u^{2}=k m . k e[\mathrm{km}\) and ke are magnetic and dielectric di - constants]

as medium is non diamagnetic, \(k m=1\)

\(\Rightarrow k e=\mu^{2}=(2.4)^{2} \Rightarrow k e=5.76\)