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

Given equation of wave 

$\vec{E}={\vec{E}}_0(4\times \overrightarrow{10}x-50t)$

Comparing with general equation of wave,

$\vec{E}={\vec{E}}_0(kx-wt),$

we get,

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

Thus velocity of wave, 

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

so, refractive index of medium,

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

using, 

$u^2=km.ke$     [km and ke are magnetic and dielectric di - constants]

as medium is non diamagnetic, $km=1$

$\Rightarrow ke={\mu }^2=(2.4{)}^2\Rightarrow ke=5.76$