JEE Main 2026 — Electromagnetic Waves Question with Solution

For an electromagnetic wave, the relationship between electric and magnetic field amplitudes is $B_0=\frac{E_0}{c}$.
Here $E_0=54$ V/m and $c=3\times 10^8$ m/s.
So, $B_0=\frac{54}{3\times 10^8}=1.8\times 10^{-7}$ T.
The electric field is along the $\hat{j}$ direction.
Since the wave travels in the $+z$ direction, the magnetic field direction is determined by $\vec{E}\times \vec{B}$ pointing in the $+z$ direction.
Using the right-hand rule: $\hat{j}\times (-\hat{i})=\hat{k}$ (positive $z$ direction), confirming the magnetic field is in the $-\hat{i}$ direction.
Therefore, $\vec{B}=-1.8\times 10^{-7}\sin (kz-\omega t)\hat{i}$ T.