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 step by step, we will address both parts: the direction of the electric and magnetic field vectors and the calculation of the wavelength.

### Step 1: Determine the directions of the electric and magnetic field vectors.
Since the electromagnetic wave is traveling in the z-direction, we can use the right-hand rule to determine the directions of the electric field (E) and magnetic field (B) vectors.

- The electric field vector (E) can be oriented along the x-axis.
- The magnetic field vector (B) will then be oriented along the y-axis.

Thus, we have:
- E is in the x-direction.
- B is in the y-direction.

### Step 2: Calculate the wavelength of the wave.
To find the wavelength (λ) of the electromagnetic wave, we use the formula:

\[ \lambda = \frac{c}{f} \]

where:
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).
- \( f \) is the frequency of the wave.

Given that the frequency \( f = 30 \, \text{MHz} = 30 \times 10^6 \, \text{Hz} \), we can substitute the values into the formula:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{30 \times 10^6 \, \text{Hz}} \]

### Step 3: Perform the calculation.
Now, we simplify the expression:

\[ \lambda = \frac{3 \times 10^8}{30 \times 10^6} = \frac{3}{30} \times \frac{10^8}{10^6} = \frac{1}{10} \times 10^2 = 10 \, \text{m} \]

### Conclusion:
The wavelength of the wave is \( 10 \, \text{m} \).

### Summary of Results:
- The electric field vector (E) is in the x-direction.
- The magnetic field vector (B) is in the y-direction.
- The wavelength of the wave is \( 10 \, \text{m} \).

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