The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
$E_x=E_0 \sin (kz - wt)$
$B_y= B_0 \sin (kz-wt)$
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field $E_x$ and magnetic field $B_y$ are perpendicular to each other and perpendicular to the z-direction.
(C) The electric and magnetic fields $E_x$ and $B_y$ are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length $λ$ of the wave by the usual equation $k = λ/2 π$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (B) only
Given: $E_x = E_0 \sin(kz - \omega t)$ and $B_y = B_0 \sin(kz - \omega t)$
(A) The wave propagates in the $+z$ direction because phase is $(kz - \omega t)$ → Correct.
(B) $E$ is along $x$-axis, $B$ along $y$-axis, propagation along $z$-axis. They are mutually perpendicular → Correct.
(C) $E$ and $B$ are perpendicular to each other but not parallel to propagation. They are both ⟂ to $z$ → Wrong.
(D) Wave number $k = \frac{2\pi}{\lambda}$, not $\frac{\lambda}{2\pi}$ → Wrong.
Correct statements: (A), (B)