A plane electromagnetic wave travels in vacuum along \( z \)-direction. What will be the directions of its electric field (\( \vec{E} \)) and magnetic field (\( \vec{B} \)) vectors?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \vec{E} \) and \( \vec{B} \) in \( x \)-\( y \) plane and are mutually perpendicular
An electromagnetic wave is transverse: \( \vec{E} \) and \( \vec{B} \) are both perpendicular to the direction of propagation and perpendicular to each other, with \( \vec{E}\times\vec{B} \) along the direction of travel.
The wave travels along \( z \), so both fields must lie in the plane perpendicular to \( z \), which is the \( x \)-\( y \) plane. For example, \( \vec{E} \) along \( x \) and \( \vec{B} \) along \( y \) gives \( \hat{\imath}\times\hat{\jmath} = \hat{k} \).
Option (1) \( \vec{E} \) and \( \vec{B} \) in \( y \)-\( z \) plane and are mutually perpendicular — Incorrect. The \( y \)-\( z \) plane contains the direction of travel \( z \).
Option (2) \( \vec{E} \) and \( \vec{B} \) in \( z \)-\( x \) plane and are mutually perpendicular — Incorrect. The \( z \)-\( x \) plane also contains the direction of travel.
Option (4) \( \vec{E} \) and \( \vec{B} \) in \( x \)-\( z \) plane and are mutually parallel — Incorrect. \( \vec{E} \) and \( \vec{B} \) are never parallel in an electromagnetic wave, and the \( x \)-\( z \) plane contains the direction of travel.
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 – “… The electric and magnetic fields Ex and By are perpendicular to each other, and to the direction z of propagation.”