If the directions of electric and magnetic field vectors of a plane electromagnetic wave are along positive y- direction and positive z-direction respectively , then the direction of propagation of the wave is along

Options

A. Positive z - direction
B. Negative z - direction
C. Negative y - direction
D. Positive x - direction

Answer

To determine the direction of propagation of an electromagnetic wave given the directions of the electric field (E) and magnetic field (B), we can use the right-hand rule and the cross product of the two vectors.

### Step-by-Step Solution:

1. **Identify the Directions of E and B:**
- The electric field vector (E) is directed along the positive y-direction.
- The magnetic field vector (B) is directed along the positive z-direction.

2. **Represent the Vectors:**
- We can represent the electric field vector as \( \mathbf{E} = E \hat{j} \) (where \( \hat{j} \) is the unit vector in the y-direction).
- We can represent the magnetic field vector as \( \mathbf{B} = B \hat{k} \) (where \( \hat{k} \) is the unit vector in the z-direction).

3. **Use the Cross Product to Find the Direction of Propagation:**
- The direction of propagation of the electromagnetic wave can be found using the cross product \( \mathbf{E} \times \mathbf{B} \).
- According to the right-hand rule, if you point your fingers in the direction of \( \mathbf{E} \) (positive y-direction) and curl them towards \( \mathbf{B} \) (positive z-direction), your thumb will point in the direction of propagation.

4. **Calculate the Cross Product:**
- The cross product \( \mathbf{E} \times \mathbf{B} \) can be calculated as follows:
\[ \mathbf{E} \times \mathbf{B} = (E \hat{j}) \times (B \hat{k}) = E B (\hat{j} \times \hat{k}) \]
- From vector algebra, we know that \( \hat{j} \times \hat{k} = \hat{i} \) (where \( \hat{i} \) is the unit vector in the x-direction).

5. **Determine the Direction of Propagation:**
- Therefore, the direction of propagation of the wave is along the positive x-direction, which can be represented as \( \hat{i} \).

### Final Answer:
The direction of propagation of the wave is along the **positive x-direction**.