A light wave is travelling along `+y` axis. At a particular point on a given time, electric field vector is along `+ x` axis then the magnetic field vector is directed along:

Options

A. `- z ` axis
B. `+z ` axis
C. `-y` axis
D. `+y` axis

Explanation

To solve the problem, we need to determine the direction of the magnetic field vector when a light wave is traveling along the +y axis and the electric field vector is directed along the +x axis.

### Step-by-Step Solution:

1. **Identify the Direction of Propagation**:
The light wave is traveling along the +y axis. This means the wave vector \( \vec{C} \) is in the direction of the y-axis.

2. **Identify the Electric Field Direction**:
The electric field vector \( \vec{E} \) is given to be along the +x axis. This means \( \vec{E} \) is in the direction of the x-axis.

3. **Use the Right-Hand Rule**:
According to the electromagnetic wave propagation, the relationship between the electric field \( \vec{E} \), magnetic field \( \vec{B} \), and the direction of wave propagation \( \vec{C} \) is given by the right-hand rule:
\[ \vec{E} \times \vec{B} = \vec{C} \]
Here, \( \vec{C} \) is the direction of wave propagation.

4. **Set Up the Cross Product**:
We know:
- \( \vec{E} \) is along +x (let's denote it as \( \hat{i} \)).
- The wave is propagating in the +y direction (denote it as \( \hat{j} \)).
- We need to find \( \vec{B} \).

We can express this as:
\[ \hat{i} \times \vec{B} = \hat{j} \]

5. **Determine the Direction of \( \vec{B} \)**:
To find \( \vec{B} \), we need to determine what direction will satisfy the equation \( \hat{i} \times \vec{B} = \hat{j} \).

Using the right-hand rule:
- Point your fingers in the direction of \( \hat{i} \) (x-axis).
- Curl your fingers towards \( \hat{j} \) (y-axis).
- Your thumb will point in the direction of \( \vec{B} \).

To achieve this, \( \vec{B} \) must be in the negative z-direction (since curling from x to y goes downwards towards -z).

6. **Conclusion**:
Therefore, the magnetic field vector \( \vec{B} \) is directed along the -z axis.

### Final Answer:
The magnetic field vector is directed along the -z axis.

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