Key property of an electromagnetic wave

For a plane electromagnetic wave in free space:

• $\vec{E} \perp \vec{B}$
• both are perpendicular to the direction of propagation
• the direction of propagation is given by $\vec{E} \times \vec{B}$

Given direction of propagation

The wave propagates along the $+x$ direction. Therefore, $\vec{E} \times \vec{B} = +\hat{i}$

Also, neither $\vec{E}$ nor $\vec{B}$ can have an $x$-component, because both must be transverse to the direction of propagation.

Check each option

Option A: $E_x, B_y$

Here electric field has an $x$-component. But the wave is traveling along $+x$, so $\vec{E}$ cannot be along $x$. Hence, incorrect.

Option B: $E_y, B_x$

Here magnetic field has an $x$-component. But $\vec{B}$ must also be perpendicular to the direction of propagation. Hence, incorrect.

Option C: $E_y, B_z$

Let $\vec{E} = E_y \hat{j}, \qquad \vec{B} = B_z \hat{k}$ Then $\vec{E} \times \vec{B} = \hat{j} \times \hat{k} = \hat{i}$ which is along $+x$. Hence, correct.

Option D: $E_z, B_y$

Let $\vec{E} = E_z \hat{k}, \qquad \vec{B} = B_y \hat{j}$ Then $\vec{E} \times \vec{B} = \hat{k} \times \hat{j} = -\hat{i}$ which is along $-x$, not $+x$. Hence, incorrect.

Final answer

The correct pair is $E_y,\; B_z$

So the correct option is C.