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 (B) of an electromagnetic wave given the electric amplitude (E), we can use the relationship between the electric field and magnetic field in electromagnetic waves, which is expressed as:

\[ \frac{E}{B} = c \]

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

### Step-by-Step Solution:

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

2. **Rearrange the formula to solve for B:**
\[ B = \frac{E}{c} \]

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

4. **Perform the calculation:**
\[ B = \frac{5}{3 \times 10^8} \approx 1.6667 \times 10^{-8} \, \text{T} \]

5. **Round the result to two decimal places:**
\[ B \approx 1.67 \times 10^{-8} \, \text{T} \]

### Final Answer:
The magnetic amplitude \( B \) is approximately \( 1.67 \times 10^{-8} \, \text{T} \).