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

Options

A. `E_(y),B_(z)`
B. `E_(z),B_(y)`
C. `E_(x),B_(y)`
D. both (a) and (b)

Explanation

To solve the question regarding 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 Propagation Direction**:
- An electromagnetic wave propagating in the x-direction means that the wave travels along the x-axis.

2. **Use the Right-Hand Rule**:
- The right-hand rule states that if you point your thumb in the direction of the 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. **Analyze the Given Options**:
- **Option A**: E is in the y-direction and B is in the z-direction.
- Using the right-hand rule:
- Thumb (x-direction) → E (y-direction) → B (z-direction).
- This configuration satisfies the right-hand rule.

- **Option B**: E is in the z-direction and B is in the y-direction.
- Using the right-hand rule:
- Thumb (x-direction) → E (z-direction) → B (y-direction).
- This configuration also satisfies the right-hand rule.

- **Option C**: E is in the x-direction and B is in the y-direction.
- Using the right-hand rule:
- Thumb (x-direction) → E (x-direction) → B (y-direction).
- This configuration does not satisfy the right-hand rule because the electric field cannot be in the same direction as the propagation direction.

4. **Conclusion**:
- The valid pairs of (E, B) that satisfy the conditions for a plane electromagnetic wave propagating in the x-direction are:
- Option A: E in y-direction and B in z-direction.
- Option B: E in z-direction and B in y-direction.
- Therefore, the correct answer is that both A and B are valid configurations.

### Final Answer:
Both A and B are correct.

---