# Electromagnetic waves: are the two chiral options possible?

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}

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}

Are both cases possible?

• I see... However, in classical electromagnetic theory the only possibility would be the first one, wouldn't it? Feb 13 '20 at 13:53
• Your answer is right for electrons. Protons and positrons have not yet been explored. Feb 13 '20 at 14:26

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.