The electric field E and magnetic field B of an electromagnetic wave passing through vacuum are given by E =…

We know that the speed of a wave is given by,

$v=\frac{\mathrm{\omega }}{k} ...\left(\mathrm{i}\right)$ 

and the speed of the electromagnetic wave in vacuum is given by,

$c=\frac{E_0}{B_0} ...\left(\mathrm{ii}\right)$ 

So, the speed of the electromagnetic wave, using $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$ is,

$\frac{\mathrm{\omega }}{k}=\frac{E_0}{B_0}$ 

$\Rightarrow E_{0}k=B_0\mathrm{\omega }$.