The magnetic field In a travelling electromagnetic wave has a peak value of `20 n T ` The peak value of electric field strength is :

Options

A. `6 V//m`
B. `9 V//m`
C. `12 V//m`
D. `3 V//m`

Answer

To solve the problem, we need to find the peak value of the electric field strength (E₀) given the peak value of the magnetic field (B₀) in a traveling electromagnetic wave. The relationship between the electric field and magnetic field in an electromagnetic wave is given by the equation:

\[ E₀ = c \cdot B₀ \]

where:
- \( E₀ \) is the peak value of the electric field strength,
- \( B₀ \) is the peak value of the magnetic field strength,
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \) m/s.

### Step-by-step Solution:

1. **Convert the magnetic field strength to Tesla**:
Given the peak value of the magnetic field \( B₀ = 20 \, nT \):
\[ B₀ = 20 \, nT = 20 \times 10^{-9} \, T \]

2. **Use the speed of light**:
The speed of light \( c \) is:
\[ c = 3 \times 10^8 \, m/s \]

3. **Calculate the peak value of the electric field strength**:
Substitute the values of \( c \) and \( B₀ \) into the equation \( E₀ = c \cdot B₀ \):
\[ E₀ = (3 \times 10^8 \, m/s) \cdot (20 \times 10^{-9} \, T) \]

4. **Perform the multiplication**:
\[ E₀ = 3 \times 20 \times 10^{8 - 9} = 60 \times 10^{-1} = 6 \, V/m \]

5. **Final answer**:
The peak value of the electric field strength is:
\[ E₀ = 6 \, V/m \]

### Summary:
The peak value of the electric field strength is \( 6 \, V/m \).