The electric field in a plane electromagnetic wave is given by, E =...

The equation of electric field is given in the question, $E = 50\sin \left(500x - 10 \times {10}^{10}t\right)V{m}^{- 1}$ now compare it the equation of electric field in an electromagnetic wave, $E = {E}_{0}\sin \left(kx - \omegat\right)V{m}^{- 1}$

$⇒ \omega = {10}^{10}rad{s}^{- 1}$ and, $k = 50{m}^{- 1}$, so the velocity of electromagnetic waves is, $v = \dfrac{\omega}{k} = \dfrac{{10}^{10}}{50} = 2 \times {10}^{8} = \dfrac{2}{3}c$.