In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of `2xx10^(10)Hz` and amplitude `48V//m`. The wavelength of the wave will be-

Options

A. `24 xx 10^(-10) m`
B. `1.5 xx 10^(-2) m`
C. `4.16 xx 10^(8) m`
D. `3 xx 10^(8)m`

Explanation

To find the wavelength of the electromagnetic wave given its frequency and amplitude, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency (f) = \(2 \times 10^{10} \, \text{Hz}\)
- Amplitude (not needed for wavelength calculation) = \(48 \, \text{V/m}\)
- Speed of light (c) = \(3 \times 10^{8} \, \text{m/s}\)

2. **Use the Relationship Between Speed, Frequency, and Wavelength:**
The relationship is given by the formula:
\[ v = f \lambda \]
Where:
- \(v\) is the speed of the wave (for electromagnetic waves, this is the speed of light, \(c\)),
- \(f\) is the frequency,
- \(\lambda\) is the wavelength.

3. **Rearrange the Formula to Solve for Wavelength (\(\lambda\)):**
We can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]
Since \(v = c\) for electromagnetic waves, we can write:
\[ \lambda = \frac{c}{f} \]

4. **Substitute the Known Values:**
Now, substitute the values of \(c\) and \(f\) into the equation:
\[ \lambda = \frac{3 \times 10^{8} \, \text{m/s}}{2 \times 10^{10} \, \text{Hz}} \]

5. **Calculate the Wavelength:**
Performing the division:
\[ \lambda = \frac{3 \times 10^{8}}{2 \times 10^{10}} = \frac{3}{2} \times 10^{-2} \, \text{m} \]
Simplifying this gives:
\[ \lambda = 1.5 \times 10^{-2} \, \text{m} \]

6. **Final Result:**
Therefore, the wavelength of the wave is:
\[ \lambda = 0.015 \, \text{m} \text{ or } 1.5 \, \text{cm} \]