Nature of EM Waves & Wave Equation question from JEE Main 2018 (16 Apr, Shift 1)

Answer: (a)

1. Wave along $+y$: phase must be $(y - ct)$, which rules out (b).
2. Intensity $I = \frac{1}{2}\varepsilon_0 c E_0^2 \Rightarrow E_0 = \sqrt{\dfrac{2I}{\varepsilon_0 c}}$, which rules out (c) and (d).
3. Check direction: $\vec{E} \parallel \hat{k}$, $\vec{B} \parallel \hat{i}$ gives $\hat{k} \times \hat{i} = \hat{j}$, along propagation; $B = E/c$.
4. So the answer is (a).