An electromagnetic wave is transporting energy in the negative y-direction. At one point and at one instant, the magnetic field is in the positive x-direction. The electric field at that point and instant is in the
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → negative z-direction
The fields \( \vec{E} \) and \( \vec{B} \) of an electromagnetic wave are perpendicular to each other and to the direction of propagation. Also, \( \vec{E}\times\vec{B} \) points along the direction of propagation. Here \( \vec{B} \) is along \( +\hat{\imath} \) and the wave travels along \( -\hat{\jmath} \).
Option (1) positive y-direction — Incorrect. The y-axis is the line along which the wave travels, and \( \vec{E} \) is perpendicular to it.
Option (2) negative y-direction — Incorrect. This is the direction in which the wave carries energy. \( \vec{E} \) must be perpendicular to this direction.
Option (3) positive z-direction — Incorrect. \( \hat{k}\times\hat{\imath}=\hat{\jmath} \), so this \( \vec{E} \) with \( \vec{B} \) along +x would belong to a wave travelling along +y.
Option (4) negative z-direction — Correct. Being perpendicular to both \( \vec{B} \) (x-axis) and the travel (y-axis), \( \vec{E} \) must lie along the z-axis. Its sign follows from \( (-\hat{k})\times\hat{\imath}=-\hat{\jmath} \), the direction in which the energy flows.
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 – “To find the direction, we note that E is along y-direction and the wave propagates along x-axis. Therefore, B should be in a direction perpendicular to both x- and y-axes. Using vector algebra, E × B should be along x-direction.”