A plane electromagnetic wave travels in vacuum along z- direction. What can you say about the directions of ots electric and magnetic field vectors. If the frequency of the wave is `30 MHz`, what is its wavelength?

Explanation

To solve the problem, we will break it down into two parts:

1. Determining the directions of the electric and magnetic field vectors.
2. Calculating the wavelength of the electromagnetic wave given its frequency.

### Step 1: Determine the Directions of the Electric and Magnetic Field Vectors

- **Given**: The electromagnetic wave travels in the z-direction.
- **Understanding Electromagnetic Waves**: In an electromagnetic wave, the electric field (E) and magnetic field (B) are always perpendicular to each other and also perpendicular to the direction of wave propagation.
- **Direction Analysis**:
- If the wave is traveling in the z-direction, the electric field vector can be oriented along the x-axis.
- Consequently, the magnetic field vector will be oriented along the y-axis.

**Conclusion for Step 1**:
- The electric field vector (E) is along the x-axis.
- The magnetic field vector (B) is along the y-axis.

### Step 2: Calculate the Wavelength

- **Given**: Frequency (f) = 30 MHz = 30 × 10^6 Hz.
- **Formula for Wavelength**: The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{c}{f} \]
where \( c \) is the speed of light in vacuum, approximately \( 3 × 10^8 \) m/s.

- **Calculation**:
\[ \lambda = \frac{3 × 10^8 \text{ m/s}}{30 × 10^6 \text{ Hz}} \]
\[ \lambda = \frac{3 × 10^8}{30 × 10^6} = \frac{3}{30} × 10^{8-6} = \frac{1}{10} × 10^2 = 10 \text{ meters} \]

**Conclusion for Step 2**:
- The wavelength of the electromagnetic wave is 10 meters.

### Final Answer:
1. The electric field vector is along the x-axis, and the magnetic field vector is along the y-axis.
2. The wavelength of the wave is 10 meters.