If `E` and `B` represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of eletromagnetic wave is along.

Options

A. E
B. B
C. `Bxx E`
D. `E xx B`

Answer

To determine the direction of propagation of an electromagnetic wave given the electric field vector \( \mathbf{E} \) and the magnetic field vector \( \mathbf{B} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Orientation of Vectors**:
- The electric field vector \( \mathbf{E} \) and the magnetic field vector \( \mathbf{B} \) are perpendicular to each other in an electromagnetic wave. We can visualize this in a three-dimensional coordinate system where \( \mathbf{E} \) is along one axis (say the x-axis) and \( \mathbf{B} \) is along another axis (say the y-axis).

2. **Use the Right-Hand Rule**:
- To find the direction of propagation of the electromagnetic wave, we can use the right-hand rule. Point your right thumb in the direction of the electric field vector \( \mathbf{E} \) and your index finger in the direction of the magnetic field vector \( \mathbf{B} \). Your middle finger, when extended perpendicular to the other two fingers, will point in the direction of wave propagation \( \mathbf{k} \).

3. **Determine the Direction of Propagation**:
- If we assume \( \mathbf{E} \) is in the positive x-direction and \( \mathbf{B} \) is in the positive y-direction, then using the right-hand rule, the direction of propagation \( \mathbf{k} \) will be in the positive z-direction.

4. **Cross Product Representation**:
- Mathematically, the direction of propagation can be expressed using the cross product:
\[ \mathbf{k} \propto \mathbf{E} \times \mathbf{B} \]
- This means that the direction of the wave vector \( \mathbf{k} \) is given by the cross product of \( \mathbf{E} \) and \( \mathbf{B} \).

5. **Conclusion**:
- Therefore, the direction of propagation of the electromagnetic wave is along the positive z-axis if \( \mathbf{E} \) is along the x-axis and \( \mathbf{B} \) is along the y-axis.

### Final Answer:
The direction of propagation of the electromagnetic wave is along the positive z-axis.

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