A plane polarized electromagnetic wave of frequency `6xx10^(8)`Hz is propagating through a region of space. Electric field is along positive z-direction and magnetic field is along positive y-direction at some instant. The peak value of electric field is 3 milli-volt/m.
The direction of propagation of wave is

Options

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

Answer

To determine the direction of propagation of the electromagnetic wave, we can use the relationship between the electric field (E), magnetic field (B), and the direction of wave propagation (k).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Frequency of the wave, \( f = 6 \times 10^8 \) Hz.
- Electric field \( \mathbf{E} \) is along the positive z-direction.
- Magnetic field \( \mathbf{B} \) is along the positive y-direction.
- Peak value of electric field \( E_0 = 3 \) mV/m.

2. **Understand the Orientation of Fields:**
- The electric field vector \( \mathbf{E} \) can be represented as:
\[ \mathbf{E} = E_0 \hat{k} \quad (\text{where } \hat{k} \text{ is the unit vector in the z-direction}) \]
- The magnetic field vector \( \mathbf{B} \) can be represented as:
\[ \mathbf{B} = B_0 \hat{j} \quad (\text{where } \hat{j} \text{ is the unit vector in the y-direction}) \]

3. **Use the Right-Hand Rule:**
- In electromagnetic waves, the direction of propagation \( \mathbf{k} \) can be determined using the right-hand rule, which states that if you point your thumb in the direction of the electric field \( \mathbf{E} \) and your fingers in the direction of the magnetic field \( \mathbf{B} \), your palm will face in the direction of wave propagation \( \mathbf{k} \).
- Here, if \( \mathbf{E} \) is in the z-direction and \( \mathbf{B} \) is in the y-direction, then:
- Thumb points in the z-direction (E).
- Fingers point in the y-direction (B).
- Palm will face in the x-direction (propagation direction).

4. **Conclusion:**
- Therefore, the direction of propagation of the wave is along the positive x-direction.

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

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