The electric field in a plane electromagnetic wave is given by, E = 50 sin 500 x - 10 × 10 10 t   V   m - 1 . The velocity of an electromagnetic wave in this medium is: (Given c = the speed of light in vacuum).

Step-by-step solution

The equation of electric field is given in the question, E = 50 sin 500 x - 10 × 10 10 t   V   m - 1 now compare it the equation of electric field in an electromagnetic wave, E = E 0 sin k x - ω t   V   m - 1 ⇒ ω = 10 10   rad   s - 1 and, k = 50   m - 1 , so the velocity of electromagnetic waves is, v = ω k = 10 10 50 = 2 × 10 8 = 2 3 c .