In an electromagnetic wave, the amplitude of magnetic field is `3xx10^(-10)T`. If the frequency of the waves is `10^(12)Hz` , then the amplitude of the associated electrical field will be :-

Options

A. `9xx10^(-2)V//m`
B. `3xx10^(-2)V//m`
C. `3xx10^(-10)V//m`
D. `9V//m`

Explanation

To find the amplitude of the associated electric field (E₀) in an electromagnetic wave given the amplitude of the magnetic field (B₀) and the frequency (f), we can use the relationship between the electric field and magnetic field in an electromagnetic wave. The relationship is given by:

\[ E_0 = c \cdot B_0 \]

where:
- \( E_0 \) is the amplitude of the electric field,
- \( B_0 \) is the amplitude of the magnetic field,
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step-by-Step Solution:

1. **Identify the given values**:
- Amplitude of the magnetic field, \( B_0 = 3 \times 10^{-10} \, \text{T} \)
- Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the formula to find the electric field amplitude**:
\[ E_0 = c \cdot B_0 \]

3. **Substitute the values into the equation**:
\[ E_0 = (3 \times 10^8 \, \text{m/s}) \cdot (3 \times 10^{-10} \, \text{T}) \]

4. **Calculate the product**:
\[ E_0 = 3 \times 3 \times 10^8 \times 10^{-10} = 9 \times 10^{-2} \, \text{V/m} \]

5. **Final result**:
The amplitude of the associated electric field is:
\[ E_0 = 9 \times 10^{-2} \, \text{V/m} \]