In an electromagnetic wave, the electric field oscillated sinusoidally with amplitude `45 V//m^(-1)`. The RMS value of oscillating magnetic field will be:

Options

A. `1.6xx10^(-8)` T
B. `16xx10^(-9)` T
C. `144xx10^(8)` T
D. `11.3xx10^(-8)` T

Explanation

To find the RMS value of the oscillating magnetic field in an electromagnetic wave where the electric field oscillates sinusoidally with a given amplitude, we can follow these steps:

### Step 1: Identify the given values
We are given:
- Amplitude of the electric field, \( E_0 = 45 \, \text{V/m} \)
- Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \)

### Step 2: Relate the electric field to the magnetic field
In electromagnetic waves, the relationship between the electric field \( E \) and the magnetic field \( B \) is given by the equation:
\[ c = \frac{E}{B} \]
From this, we can express the magnetic field \( B \) in terms of the electric field \( E \):
\[ B = \frac{E}{c} \]

### Step 3: Calculate the peak magnetic field \( B_0 \)
Substituting the values into the equation:
\[ B_0 = \frac{E_0}{c} = \frac{45 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} = 15 \times 10^{-8} \, \text{T} \]

### Step 4: Calculate the RMS value of the magnetic field
The RMS (Root Mean Square) value of the magnetic field \( B_{\text{RMS}} \) is related to the peak magnetic field \( B_0 \) by the formula:
\[ B_{\text{RMS}} = \frac{B_0}{\sqrt{2}} \]
Substituting the value of \( B_0 \):
\[ B_{\text{RMS}} = \frac{15 \times 10^{-8} \, \text{T}}{\sqrt{2}} \approx \frac{15 \times 10^{-8}}{1.414} \approx 10.6 \times 10^{-8} \, \text{T} \]

### Step 5: Final approximation
Rounding \( 10.6 \times 10^{-8} \, \text{T} \) gives us approximately:
\[ B_{\text{RMS}} \approx 11.0 \times 10^{-8} \, \text{T} \]

### Conclusion
The RMS value of the oscillating magnetic field is approximately \( 11.0 \times 10^{-8} \, \text{T} \).