Question

For an electromagnetic wave propagating through vacuum, \( \vec{k},\vec{E}\) and \( \omega \) represent propagation vector, electric field and angular frequency respectively. The magnetic field associated with this wave is represented by :

• A. \( \dfrac{\vec{E}\times\vec{k}}{\omega} \)
• B. \( \dfrac{\vec{k}\times\vec{E}}{\omega} \)
• C. \( \omega(\vec{E}\times\vec{k}) \)
• D. \( \omega(\vec{k}\times\vec{E}) \)

Answer 1

The Correct Option is B

Concept: For a plane electromagnetic wave in vacuum: \[ \vec{B} = \frac{1}{\omega}(\vec{k}\times\vec{E}) \] where

• \( \vec{k} \) is the propagation vector
• \( \vec{E} \) is the electric field
• \( \omega \) is angular frequency

Step 1: {Recall Maxwell's relation.} For electromagnetic waves: \[ \vec{k}\cdot\vec{E}=0 \] \[ \vec{k}\cdot\vec{B}=0 \] Thus \( \vec{E},\vec{B},\vec{k} \) are mutually perpendicular. Step 2: {Write magnetic field expression.} \[ \vec{B}=\frac{\vec{k}\times\vec{E}}{\omega} \] Thus the correct representation is \[ \frac{\vec{k}\times\vec{E}}{\omega} \]