The amplitude of the electric field of a plane electromagnetic wave in air is `6.0 xx 10 ^(-4) V m ^(-1). ` The amplitude of the magnetic field will be

Options

A. `1.8 xx 10 ^(5)T`
B. `5.0 xx 10 ^(3) T`
C. `1.0 xx 10 ^(-4) T`
D. `2.0 xx 10 ^(-12) T`

Explanation

To find the amplitude of the magnetic field (B₀) of a plane electromagnetic wave given the amplitude of the electric field (E₀), we can use the relationship between the electric field and the magnetic field in electromagnetic waves. The relationship is given by the equation:

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

where:
- \( B_0 \) is the amplitude of the magnetic field,
- \( E_0 \) is the amplitude of the electric field,
- \( c \) is the speed of light in vacuum (approximately \( 3.0 \times 10^8 \, \text{m/s} \)).

### Step-by-Step Solution:

1. **Identify the given values:**
- Amplitude of the electric field, \( E_0 = 6.0 \times 10^{-4} \, \text{V/m} \)
- Speed of light, \( c = 3.0 \times 10^8 \, \text{m/s} \)

2. **Use the formula to find B₀:**
\[ B_0 = \frac{E_0}{c} \]

3. **Substitute the known values into the equation:**
\[ B_0 = \frac{6.0 \times 10^{-4} \, \text{V/m}}{3.0 \times 10^8 \, \text{m/s}} \]

4. **Perform the calculation:**
\[ B_0 = \frac{6.0}{3.0} \times \frac{10^{-4}}{10^8} = 2.0 \times 10^{-12} \, \text{T} \]

5. **Final result:**
The amplitude of the magnetic field \( B_0 \) is \( 2.0 \times 10^{-12} \, \text{T} \).