The mean intensity of radiation on the surface of the Sun is about `10^(s)W//m^2`. The rms value of the corresponding magnetic field is closed to :

Options

A. 1T
B. `10^2T`
C. `10^(-2)T`
D. `10^(-4)T`

Explanation

To find the root mean square (RMS) value of the magnetic field corresponding to the mean intensity of radiation on the surface of the Sun, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship Between Intensity and Electric Field**:
The intensity \( I \) of electromagnetic radiation is related to the RMS value of the electric field \( E_{\text{rms}} \) by the equation:
\[ I = \epsilon_0 c E_{\text{rms}}^2 \]
where \( \epsilon_0 \) is the permittivity of free space and \( c \) is the speed of light.

2. **Relating Electric Field to Magnetic Field**:
The RMS value of the electric field \( E_{\text{rms}} \) is also related to the RMS value of the magnetic field \( B_{\text{rms}} \) by the equation:
\[ E_{\text{rms}} = c B_{\text{rms}} \]

3. **Substituting the Electric Field into the Intensity Equation**:
Substitute \( E_{\text{rms}} = c B_{\text{rms}} \) into the intensity equation:
\[ I = \epsilon_0 c (c B_{\text{rms}})^2 \]
This simplifies to:
\[ I = \epsilon_0 c^3 B_{\text{rms}}^2 \]

4. **Solving for \( B_{\text{rms}} \)**:
Rearranging the equation to solve for \( B_{\text{rms}} \):
\[ B_{\text{rms}}^2 = \frac{I}{\epsilon_0 c^3} \]
Taking the square root gives:
\[ B_{\text{rms}} = \sqrt{\frac{I}{\epsilon_0 c^3}} \]

5. **Substituting Known Values**:
We know:
- The mean intensity \( I \) on the surface of the Sun is approximately \( 10^8 \, \text{W/m}^2 \).
- The permittivity of free space \( \epsilon_0 \approx 8.854 \times 10^{-12} \, \text{F/m} \).
- The speed of light \( c \approx 3 \times 10^8 \, \text{m/s} \).

Now substituting these values into the equation:
\[ B_{\text{rms}} = \sqrt{\frac{10^8}{8.854 \times 10^{-12} \times (3 \times 10^8)^3}} \]

6. **Calculating the Denominator**:
First, calculate \( (3 \times 10^8)^3 \):
\[ (3 \times 10^8)^3 = 27 \times 10^{24} \, \text{m}^3/\text{s}^3 \]
Now multiply by \( \epsilon_0 \):
\[ 8.854 \times 10^{-12} \times 27 \times 10^{24} \approx 2.39 \times 10^{13} \]

7. **Final Calculation**:
Now substitute back into the equation:
\[ B_{\text{rms}} = \sqrt{\frac{10^8}{2.39 \times 10^{13}}} \approx \sqrt{4.18 \times 10^{-6}} \approx 2.04 \times 10^{-3} \, \text{T} \]
This value is approximately \( 10^{-4} \, \text{T} \).

### Conclusion:
Thus, the RMS value of the corresponding magnetic field is approximately \( 10^{-4} \, \text{T} \).