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Step-by-step Explanation
Step 1: Recall the Direction Properties of Electromagnetic Waves
In an electromagnetic (EM) wave, the electric field vector $ \overrightarrow{E} $, the magnetic field vector $ \overrightarrow{B} $, and the direction of propagation (given by the wave vector $ \overrightarrow{k} $) are mutually perpendicular to each other. This means:
1. $ \overrightarrow{E} \perp \overrightarrow{B} $
2. $ \overrightarrow{E} \perp \overrightarrow{k} $
3. $ \overrightarrow{B} \perp \overrightarrow{k} $
Step 2: Identify the Direction of Wave Propagation
The problem states that the EM wave is propagating along the y-direction. Hence, the wave vector $ \overrightarrow{k} $ points along the y-axis. From the perpendicularity rules, both $ \overrightarrow{E} $ and $ \overrightarrow{B} $ must lie in the plane perpendicular to the y-axis (i.e., in the x-z plane).
Step 3: Possible Orientations of $ \overrightarrow{E} $ and $ \overrightarrow{B} $
Since $ \overrightarrow{E} $ and $ \overrightarrow{B} $ must be perpendicular to each other, there are two possible scenarios that satisfy both perpendicularity to the y-axis and mutual perpendicularity:
$ \overrightarrow{E} $ along x and $ \overrightarrow{B} $ along z
$ \overrightarrow{E} $ along z and $ \overrightarrow{B} $ along x
Thus, if the wave propagates along the y-direction, $ \overrightarrow{E} $ could be in the x-direction and $ \overrightarrow{B} $ in the z-direction, or vice versa.
Step 4: Final Answer
Therefore, the correct pair of electric and magnetic field components for a plane EM wave propagating along the y-direction is:
Ex, Bz or Ez, Bx.
