JEE Main · 2020 · 09 Jan 2020 · Shift 2 · EM Waves

For a plane wave the fields and the direction of travel form a right-handed set, with $\vec{E}\times \vec{B}$ pointing along the propagation direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$. With the polarization (the $\vec{E}$ direction) along $\hat{k}$, the magnetic field must lie along $\frac{\hat{i}-\hat{j}}{\sqrt{2}}$, since $\hat{k}\times \frac{\hat{i}-\hat{j}}{\sqrt{2}}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$ returns the travel direction. A wave advancing along $+\frac{\hat{i}+\hat{j}}{\sqrt{2}}$ carries the phase $\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cdot \vec{r}$, so its magnetic field is $B_0\frac{\hat{i}-\hat{j}}{\sqrt{2}}\cos \left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$.