In an electromagnetic wave, at an anstant and at a particular position , the electric field is along the negative z-axis and magnetic field is along the positive x-axis .Then the direction of propagation of electromagnetic wave is :

Options

A. positive y-axis
B. negative y-axis
C. at `45^@` angle from positive y-axis
D. positive z-axis

Answer

To determine the direction of propagation of an electromagnetic wave given the orientations of the electric field (E) and the 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 (E) is given to be along the negative z-axis. We can represent this as:
\[ \vec{E} = -E \hat{z} \]
- The magnetic field (B) is along the positive x-axis. We can represent this as:
\[ \vec{B} = B \hat{x} \]

2. **Use the Right-Hand Rule**:
- The direction of propagation of an electromagnetic wave is given by the cross product of the electric field and the magnetic field:
\[ \vec{k} \propto \vec{E} \times \vec{B} \]
- To find the direction of \(\vec{E} \times \vec{B}\), we can use the right-hand rule. Point your fingers in the direction of \(\vec{E}\) (negative z-axis) and curl them towards \(\vec{B}\) (positive x-axis).

3. **Calculate the Cross Product**:
- The cross product \(\vec{E} \times \vec{B}\) can be calculated as follows:
\[ \vec{E} \times \vec{B} = (-E \hat{z}) \times (B \hat{x}) \]
- Using the properties of the cross product:
\[ \hat{z} \times \hat{x} = -\hat{y} \]
- Therefore:
\[ \vec{E} \times \vec{B} = -EB (\hat{z} \times \hat{x}) = -EB (-\hat{y}) = EB \hat{y} \]

4. **Determine the Direction of Propagation**:
- Since \(\vec{E} \times \vec{B}\) gives us a vector in the positive y-direction, the direction of propagation of the electromagnetic wave is along the positive y-axis.

5. **Final Answer**:
- Thus, the direction of propagation of the electromagnetic wave is along the positive y-axis.