Q 12-08-034JEE MainJEE Main 2026 (4 Apr, Shift 2)Medium
A magnetic field vector in an electromagnetic wave is represented by $\vec{B} = B_0\sin\left(2\pi vt - \dfrac{2\pi x}{\lambda}\right)\hat{j}$. Its associated electric field vector is ______.
Answer: (A) $\vec{E} = -v\lambda B_0\sin\left(2\pi vt - \frac{2\pi x}{\lambda}\right)\hat{k}$
The wave travels along $+x$, so $\vec{E} \times \vec{B}$ must point along $+\hat{i}$. With $\vec{B}$ along $\hat{j}$: $(-\hat{k}) \times \hat{j} = \hat{i}$, so $\vec{E}$ is along $-\hat{k}$.
Magnitude: $E_0 = cB_0 = v\lambda B_0$ (here $v$ is the frequency).
$\vec{E} = -v\lambda B_0\sin\left(2\pi vt - \dfrac{2\pi x}{\lambda}\right)\hat{k}$.
Solution by Sreeraj P, M.Sc Physics