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)
Answer & explanation
Correct answer: option 2
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 = $2 \times 10^8\ \text{m/s}=0.67c$