Q 12-08-226JEE MainJEE Main 2017 (8 Apr)Medium
Magnetic field in a plane electromagnetic wave is given by $\vec B = B_0\sin(kx + \omega t)\hat j$ T. Expression for corresponding electric field will be (where $c$ is speed of light):
Answer: (C) $\vec E = B_0c\sin(kx + \omega t)\hat k\ \text{V m}^{-1}$
The phase $kx + \omega t$ means the wave travels along $-x$. In an EM wave $\vec E$, $\vec B$ and the propagation direction satisfy: $\vec E\times\vec B$ is along the direction of travel, and $E_0 = cB_0$ with $E$ and $B$ in phase.
With $\vec B$ along $\hat j$, $\vec E$ must be along $\pm\hat k$. Since $\hat k\times\hat j = -\hat i$, $\vec E$ is along $+\hat k$:
$$\vec E = B_0c\sin(kx + \omega t)\hat k\ \text{V m}^{-1}$$
Solution by Sreeraj P, M.Sc Physics