JEE Main 2026 — Electromagnetic Waves Question with Solution

For an electromagnetic wave, the direction of wave propagation $\hat{k}$ is along the direction of $\vec{E}\times \vec{B}$.

Since $\vec{E}$, $\vec{B}$, and $\vec{k}$ form a mutually perpendicular right-handed system, the direction of the magnetic field is given by $\hat{B}=\hat{k}\times \hat{E}$.

The magnitudes of the electric and magnetic fields are related by $B=\frac{E}{c}$.

Using the relation for the speed of light $c=\frac{\omega }{k}$, we get $B=\frac{kE}{\omega }$.

Combining the magnitude and direction gives:

$\vec{B}=B\hat{B}=\frac{kE}{\omega }(\hat{k}\times \hat{E})$

Since $\vec{k}=k\hat{k}$ and $\vec{E}=E\hat{E}$, this simplifies to:

$\vec{B}=\frac{\vec{k}\times \vec{E}}{\omega }$

Answer: $\frac{\vec{k}\times \vec{E}}{\omega }$