A plane electromagnetic wave propagating in a non magnetic dielectric medium is given by $E=E_0\sin [2\times {10}^{-7}x-50t]$, where $\text{'}x\text{'}$ is in meter and $\text{'}t\text{'}$ is in second. If the relative permeability of the medium ${\mu }_r=1$ then the dielectric constant of the medium is

Speed of electromagnetic wave in Vacuum is  $C=\frac{1}{\sqrt{{\mu }_0{\in }_0}}$
Speed of electromagnetic wave in a dielectric medium of dielectric constant (k) is given by  $C\text{'}=\frac{1}{\sqrt{k{\mu }_0{\in }_0}}=\frac{C}{\sqrt{k}}$
From given equation  $C\text{'}=\frac{\omega }{k}=\frac{50}{2\times {10}^{-7}}$
$C\text{'}=\frac{5}{2}\times {10}^{8}m/s$  and  $C=3\times {10}^{8}m/s$
 $$\begin{gathered} U\sin g, \\ C\text{'}=\frac{C}{\sqrt{k}} \\ \Rightarrow \frac{5}{2}\times {10}^8=\frac{3\times {10}^8}{\sqrt{k}} \\ \Rightarrow \frac{25}{4}=\frac{9}{k} \\ \Rightarrow k=1.44 \end{gathered}$$