In a plane EM wave, the electric field oscillates, sinusoidally at a frequency of `2.5 xx10^(10) Hz` and amplitude `480 V/ m .` The amplitude of oscillating magnetic field (in multiple of `Wb/m^2)` will be

Answer

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

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

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

From this relationship, we can express the magnetic field in terms of the electric field:

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Frequency of the electric field, \( f = 2.5 \times 10^{10} \, \text{Hz} \) (not needed for this calculation).
- Amplitude of the electric field, \( E = 480 \, \text{V/m} \).
- Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \).

2. **Calculate the amplitude of the magnetic field:**
Using the formula \( B = \frac{E}{c} \):

\[ B = \frac{480 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

3. **Perform the calculation:**
\[ B = \frac{480}{3 \times 10^8} = \frac{480}{3} \times 10^{-8} = 160 \times 10^{-8} \, \text{T} \]

4. **Convert the magnetic field to Weber per meter squared:**
Since \( 1 \, \text{T} = 1 \, \text{Wb/m}^2 \):

\[ B = 160 \times 10^{-8} \, \text{Wb/m}^2 = 16 \times 10^{-7} \, \text{Wb/m}^2 \]

5. **Final answer:**
The amplitude of the oscillating magnetic field is \( 16 \times 10^{-7} \, \text{Wb/m}^2 \).