JEE Main 2026 — Electromagnetic Waves Question with Solution

The direction of propagation of an electromagnetic wave is given by the direction of $\vec{E}\times \vec{B}$.

Given that the wave travels along the $x$-direction, the direction of propagation is $\hat{i}$.

The magnetic field is given as $\vec{B}=2\times 10^{-7}\hat{j}$ T, so its direction is $\hat{j}$.

Let the direction of the electric field be $\hat{n}$. We must have:

$\hat{n}\times \hat{j}=\hat{i}$

Since $(-\hat{k})\times \hat{j}=\hat{i}$, the direction of the electric field is $-\hat{k}$.

The magnitude of the electric field is related to the magnetic field by $E=cB$, where $c=3\times 10^8$ m/s is the speed of light in free space.

$E=(3\times 10^8)\times (2\times 10^{-7})=60$ V/m

Therefore, the electric field vector is $\vec{E}=-60\hat{k}$ V/m.

Answer: $-60\hat{k}$