Find the value of the amplitude of the electric field if the amplitude of the magnetic field is `4xx10^7` T?

Options

A. `12 xx 10^(15) Vm^(-1)`
B. `74 xx 10^(3) Vm^(-1)`
C. `7 xx 10^(3) Vm^(-1)`
D. `17 xx 10^(3) Vm^(-1)`

Explanation

To find the value of the amplitude of the electric field (E₀) given the amplitude of the magnetic field (B₀), we can use the relationship between the electric field and the magnetic field in electromagnetic waves. 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 \( 3 \times 10^8 \) m/s.

### Step-by-Step Solution:

1. **Identify the given values**:
- Amplitude of the magnetic field, \( B_0 = 4 \times 10^{-7} \) T.
- Speed of light, \( c = 3 \times 10^8 \) m/s.

2. **Write the formula**:
\[ E_0 = c \cdot B_0 \]

3. **Substitute the values into the formula**:
\[ E_0 = (3 \times 10^8 \, \text{m/s}) \cdot (4 \times 10^{-7} \, \text{T}) \]

4. **Perform the multiplication**:
- Calculate \( 3 \times 4 = 12 \).
- Combine the powers of ten: \( 10^8 \cdot 10^{-7} = 10^{8-7} = 10^1 \).
- Therefore, \( E_0 = 12 \times 10^1 \, \text{V/m} \).

5. **Final result**:
\[ E_0 = 12 \times 10^1 \, \text{V/m} = 120 \, \text{V/m} \]

### Conclusion:
The amplitude of the electric field \( E_0 \) is \( 120 \, \text{V/m} \).

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