The electric field of a plane electromagnetic wave in a medium is given by
$E = 100 \sin (300 z - 6 × 10^{10} t) V m^{-1}$
The velocity of the electromagnetic wave in this medium will be
(Given: c - speed of light in vacuum)

0.67 c

The correct answer is Option (2) → 0.67 c

Given electric field of the wave:

$E = 100 \sin(300 z - 6 \times 10^{10} t)\ \text{V/m}$

General form of a plane EM wave: $E = E_0 \sin(k z - \omega t)$

where $k$ = wave number, $\omega$ = angular frequency, and velocity $v = \frac{\omega}{k}$

From given equation:

$k = 300\ \text{m}^{-1}$

$\omega = 6 \times 10^{10}\ \text{rad/s}$

Velocity of the wave:

$v = \frac{\omega}{k} = \frac{6 \times 10^{10}}{300} = 2 \times 10^8\ \text{m/s}$

∴ The velocity of the electromagnetic wave in this medium = $2 \times 10^8\ \text{m/s}=0.67c$