Consider an electric charge oscillating with a frequency of 10 MHz. The radiation emitted will have a wavelength equal to

Options

A. 20 m
B. 30 m
C. 40 m
D. 10 m

Answer

To find the wavelength of the radiation emitted by an oscillating electric charge with a frequency of 10 MHz, we can use the relationship between the speed of electromagnetic waves (C), frequency (f), and wavelength (λ). The formula is given by:

\[ C = f \times \lambda \]

Where:
- \( C \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) m/s.
- \( f \) is the frequency of the oscillating charge.
- \( \lambda \) is the wavelength we want to find.

### Step-by-step Solution:

1. **Identify the given frequency**:
The frequency \( f \) is given as 10 MHz. We need to convert this into standard units (Hz).
\[ f = 10 \text{ MHz} = 10 \times 10^6 \text{ Hz} = 10^7 \text{ Hz} \]

2. **Use the speed of light**:
The speed of light \( C \) is approximately:
\[ C = 3 \times 10^8 \text{ m/s} \]

3. **Rearrange the formula to solve for wavelength**:
We can rearrange the equation \( C = f \times \lambda \) to solve for \( \lambda \):
\[ \lambda = \frac{C}{f} \]

4. **Substitute the values into the equation**:
Now, substitute the values of \( C \) and \( f \) into the equation:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{10 \times 10^6 \text{ Hz}} \]

5. **Calculate the wavelength**:
Simplifying the equation gives:
\[ \lambda = \frac{3 \times 10^8}{10 \times 10^6} = \frac{3 \times 10^8}{10^7} = 30 \text{ meters} \]

### Final Answer:
The wavelength of the radiation emitted by the oscillating charge is **30 meters**.

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