Question

The electric field of an electromagnetic wave propagating in vacuum is given by $E = 35 \cos(kx - 4.5 \times 10^8 t)$ where $E_x$ and $t$ are in V/m and s respectively. The magnitude of the propagation vector $k$ is

• A. 0.5 m$^{-1}$
• B. 1 m$^{-1}$
• C. 1.5 m$^{-1}$
• D. 2 m$^{-1}$

Hint:

Use $k = \dfrac{\omega}{c}$ when the wave propagates in vacuum and angular frequency is known.

Answer 1

The Correct Option is C

The general form of a plane electromagnetic wave is: $E = E_0 \cos(kx - \omega t)$
Given: $\omega = 4.5 \times 10^8$ rad/s and wave is in vacuum
In vacuum, wave speed $c = \dfrac{\omega}{k} \Rightarrow k = \dfrac{\omega}{c}$
$c = 3 \times 10^8$ m/s, so: $k = \dfrac{4.5 \times 10^8}{3 \times 10^8} = 1.5$ m$^{-1}$