Physics - EM Waves Question with Solution | TestHub

Given $\vec{E}=E_0\cos (kz)\cos (\omega t)\hat{i}$, Maxwell's equation $\nabla \times \vec{E}=-\frac{\partial \vec{B}}{\partial t}$ gives $\vec{B}=\frac{E_0}{c}\sin (kz)\sin (\omega t)\hat{j}$.

(A) $\vec{E}$ always points along x - linearly polarized in the x-direction - correct.

(B) $\vec{B}$ oscillates along the y-direction - correct.

(C) E-nodes: $\cos (kz)=0\Rightarrow z=\frac{(2n+1)\pi }{2k}$, not $\frac{n\pi }{k}$ - incorrect.

(D) B-nodes: $\sin (kz)=0\Rightarrow z=\frac{n\pi }{k}$ - correct.

Correct options: A, B, D