A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $$\vec{E}$$ and magnetic field, $$\vec{B}$$
vectors associated with the wave in Cartesian frame are

For an electromagnetic wave propagating in the +x direction:

- The electric and magnetic fields must be perpendicular to the direction of propagation (transverse wave)

- $$\vec{E}$$, $$\vec{B}$$, and the propagation direction must form a right-handed coordinate system

Since the wave propagates along +x, neither $$\vec{E}$$ nor $$\vec{B}$$ can have an x-component.

This eliminates Options 1 (has $$E_x$$), 3 (has $$B_y$$ but we need to check), and 4 (has $$B_x$$).

For $$\hat{E} \times \hat{B} = \hat{k}_{propagation} = \hat{x}$$:

$$\hat{y} \times \hat{z} = \hat{x}$$ ✓

So $$E_y, B_z$$ is consistent with propagation along +x.

Check Option 3: $$E_z, B_y$$: $$\hat{z} \times \hat{y} = -\hat{x}$$ (propagation in -x direction). Incorrect.

The correct answer is Option 2: $$E_y, B_z$$.