A plane electromagnectic wave propagating along x-direction can have the following pairs of `E` and `B`.

Options

A. `E_x,B_y`
B. `E_y,B_z`
C. `B_x,E_y`
D. `E_z,B_y`

Explanation

To solve the problem of determining the pairs of electric field (E) and magnetic field (B) for a plane electromagnetic wave propagating along the x-direction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Direction of Propagation**:
- A plane electromagnetic wave propagating along the x-direction means that the wave travels in the positive x-direction.

2. **Identify the Electric and Magnetic Field Directions**:
- The electric field (E) and magnetic field (B) must be perpendicular to each other and also perpendicular to the direction of wave propagation (x-direction).
- According to the right-hand rule, if you point your thumb in the direction of wave propagation (x-direction), your index finger in the direction of the electric field (E), then your middle finger will point in the direction of the magnetic field (B).

3. **First Pair of Fields**:
- Let’s assume the electric field \( E \) is in the y-direction (E_y) and the magnetic field \( B \) is in the z-direction (B_z).
- According to the right-hand rule:
- Thumb (x-direction) → Wave propagation
- Index finger (y-direction) → Electric field \( E_y \)
- Middle finger (z-direction) → Magnetic field \( B_z \)
- This configuration satisfies the condition for a wave propagating in the positive x-direction.

4. **Second Pair of Fields**:
- Now, let's consider the electric field \( E \) in the z-direction (E_z) and the magnetic field \( B \) in the y-direction (B_y).
- Again applying the right-hand rule:
- Thumb (x-direction) → Wave propagation
- Index finger (z-direction) → Electric field \( E_z \)
- Middle finger (y-direction) → Magnetic field \( B_y \)
- This configuration satisfies the condition for a wave propagating in the negative x-direction.

5. **Conclusion**:
- We have identified two pairs of electric and magnetic fields:
- Pair 1: \( E_y \) and \( B_z \) (wave propagating in the positive x-direction)
- Pair 2: \( E_z \) and \( B_y \) (wave propagating in the negative x-direction)

### Final Answer:
The correct pairs of electric and magnetic fields for a plane electromagnetic wave propagating along the x-direction are:
- \( (E_y, B_z) \) for positive x-direction
- \( (E_z, B_y) \) for negative x-direction