If the electric amplitude of the electromagnetic wave is `5 V m^(-1)`, its magnetic amplitude will be

Options

A. `5 xx 10^(-8) T`
B. `1.67 xx 10^(-8)T`
C. `1.67 xx 10^(-10)T`
D. `5 xx 10^(-10)T`

Answer

To find the magnetic amplitude of an electromagnetic wave given the electric amplitude, we can use the relationship between the electric field amplitude (E) and the magnetic field amplitude (B) in an electromagnetic wave. The formula we will use is:

\[ \frac{E_0}{B_0} = c \]

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Electric field amplitude, \( E_0 = 5 \, \text{V/m} \)
- Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the formula to relate E and B**:
\[ \frac{E_0}{B_0} = c \]

3. **Rearrange the formula to solve for \( B_0 \)**:
\[ B_0 = \frac{E_0}{c} \]

4. **Substitute the known values into the equation**:
\[ B_0 = \frac{5 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

5. **Calculate \( B_0 \)**:
\[ B_0 = \frac{5}{3 \times 10^8} \]
\[ B_0 = \frac{5}{3} \times 10^{-8} \, \text{T} \]
\[ B_0 \approx 1.67 \times 10^{-8} \, \text{T} \]

6. **Final result**:
The magnetic amplitude \( B_0 \) is approximately \( 1.67 \times 10^{-8} \, \text{T} \).