An electromagnetic wave is transporting energy in the negative z direction. At certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

Options

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

Answer

To solve the problem, we need to determine the direction of the magnetic field (B) in an electromagnetic wave given the direction of the electric field (E) and the direction of wave propagation (k).

### Step-by-Step Solution:

1. **Identify the Directions**:
- The wave is propagating in the negative z-direction. This means the wave vector \( \vec{k} \) points in the negative z-direction: \( \vec{k} = -\hat{z} \).
- The electric field \( \vec{E} \) is given to be in the positive y-direction: \( \vec{E} = \hat{y} \).

2. **Use the Right-Hand Rule**:
- The relationship between the electric field \( \vec{E} \), magnetic field \( \vec{B} \), and the direction of wave propagation \( \vec{k} \) can be described using the right-hand rule. According to this rule, if you point your thumb in the direction of \( \vec{k} \) (negative z-direction) and your index finger in the direction of \( \vec{E} \) (positive y-direction), your middle finger will point in the direction of \( \vec{B} \).

3. **Apply the Right-Hand Rule**:
- Point your thumb downwards (negative z-direction).
- Point your index finger upwards (positive y-direction).
- Your middle finger will now point towards the positive x-direction.

4. **Conclusion**:
- Therefore, the direction of the magnetic field \( \vec{B} \) at that point and instant is along the positive x-direction: \( \vec{B} = \hat{x} \).

### Final Answer:
The direction of the magnetic field of the wave at that point and instant is along the positive x-direction.

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