The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\( E_x = E_0 \sin(kz - \omega t) \)
\( B_y = B_0 \sin(kz - \omega t) \)
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 \( \lambda \) of the wave by the usual equation \( k = \lambda/2\pi \)
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
A wave of the form \( \sin(kz - \omega t) \) travels along \( +z \). An electromagnetic wave is transverse: \( \vec{E} \), \( \vec{B} \) and the direction of travel are mutually perpendicular. Here \( \vec{E} \) is along \( x \) and \( \vec{B} \) along \( y \).
(A) The wave is propagating along the z-direction. — Correct. The phase \( kz - \omega t \) stays constant when \( z \) increases with \( t \), so the wave moves along \( +z \).
(B) The electric field \( E_x \) and magnetic field \( B_y \) are perpendicular to each other and perpendicular to the z-direction. — Correct. The \( x \)- and \( y \)-axes are perpendicular to each other and both are perpendicular to \( z \).
(C) The electric and magnetic fields \( E_x \) and \( B_y \) are perpendicular to each other, and parallel to the direction of propagation. — Incorrect. Being a transverse wave, neither field is along the direction of propagation.
(D) k is related to the wave length \( \lambda \) of the wave by the usual equation \( k = \lambda/2\pi \) — Incorrect. The propagation constant is \( k = 2\pi/\lambda \); the statement inverts it.
NCERT (2026-27):
Nature of Electromagnetic Waves – “It can be shown from Maxwell’s equations that electric and magnetic fields in an electromagnetic wave are perpendicular to each other, and to the direction of propagation.”
Nature of Electromagnetic Waves – “… In Fig. 8.3, we show a typical example of a plane electromagnetic wave propagating along the z direction … We can write Ex and By as follows:
\( \displaystyle E_x = E_0 \sin(kz - \omega t) \qquad [8.7(a)] \)
\( \displaystyle B_y = B_0 \sin(kz - \omega t) \qquad [8.7(b)] \)
Here k is related to the wave length λ of the wave by the usual equation
\( \displaystyle k = \frac{2\pi}{\lambda} \qquad (8.8) \)”