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Direction Of Energy Flow

Mediumphysics

A plane electromagnetic wave has its electric field oscillating along the +y axis while, at the same instant, its magnetic field oscillates along the +z axis. Along which direction does this wave transport its energy?

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About This Question

Subject
physics
Chapter
electromagnetic waves
Topic
direction of energy flow
Difficulty
Medium
Year
2025
Tags
Poynting vectorE cross Bdirection of propagationright-hand ruleenergy transport

Solution

Correct Answer:

+x direction

Energy in an electromagnetic wave travels along the direction of the Poynting vector \vec{S} = \frac{1}{\mu_0}\vec{E} \times \vec{B}, which also fixes the direction of propagation. The right-hand cross product of the field directions therefore determines where the wave moves. Taking \hat{E} along +y and \hat{B} along +z, the cross product \hat{y} \times \hat{z} = \hat{x}, so the wave propagates along the +x direction. The -x option reverses the right-hand rule incorrectly. The +z option mistakes the magnetic field direction itself for the propagation direction, which is wrong because energy flows perpendicular to both fields. The -y option similarly confuses the electric field axis with the travel direction. This vector relationship is the standard way the NCERT and JEE syllabus connect field orientation to propagation, and it holds at every instant because the two fields oscillate in phase, so their cross product never reverses sign during a cycle. Physically, this means the wave always pushes its energy forward, never momentarily backward, even as the field magnitudes rise and fall. A quick check using the cyclic order x \to y \to z confirms that y \times z indeed gives +x, so energy genuinely streams in the +x direction, consistent with the mutually perpendicular geometry of the wave.

This medium difficulty physics question is from the chapter electromagnetic waves, covering the topic of direction of energy flow. It appeared in the 2025 exam.

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