Question

The electric field of an electromagnetic wave in free space is given by \( \vec{E} = 5\sin\left(\tfrac{2\pi}{3}z - \omega t\right)\hat{y} \) V/m. Which of the following statements is correct?

• A. The wave propagates along $\hat{y}$
• B. The wave vector is given $\vec{k}=\tfrac{2\pi}{3}\hat{z}$
• C. The wavelength of the electromagnetic wave is $\frac{1}{3}$ m
• D. The corresponding magnetic field is $\vec{B}=\tfrac{5}{c}\cos(\tfrac{2\pi}{3}z-\omega t)\hat{x}$ T
• E. The frequency of the wave is approximately $10^6$ Hz

Hint:

The wave propagates in the direction of the variable inside the sine function (here, $z$). The unit vector $\hat{y}$ indicates the direction of the electric field oscillation, not the path of the wave.

Answer 1

The Correct Option is B