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Suppose we have sinusoidal electromagnetic wave travelling in the $+z$ direction. It is said that the electric field and the magnetic field must be mutually perpendicular and perpendicular to the direction of propagation. However, this leads to two possible options:

Option A: $$\begin{aligned} \vec{E}\left(x,t \right) = E_{\text{0}} \cos{\left( kx-\omega t \right)}\hat{j} \\ \vec{B}\left(x,t \right) = B_{\text{0}} \cos{\left( kx-\omega t \right)}\hat{k} \end{aligned}$$ enter image description here

Option B: $$\begin{aligned} \vec{E}\left(x,t \right) = E_{\text{0}} \cos{\left( kx-\omega t \right)}\hat{j} \\ \vec{B}\left(x,t \right) = -B_{\text{0}} \cos{\left( kx-\omega t \right)}\hat{k} \end{aligned}$$

enter image description here

Are both cases possible?

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Ok, I see that it is not. Form Maxwell's second equation, $$\nabla \times \mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}$$

So the sign of $\mathbf{B}$ is given by the sign of $\mathbf{E}$. Thus, option B would not be possible.

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  • $\begingroup$ Also Google "Poynting vector" for related information. $\endgroup$
    – The Photon
    Feb 7 '20 at 16:11

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