The number of electric lines of forces rediating from a closed surface in vacumm is `1.13xx10^(11)`. The charge enclosed by the surface is

Options

A. `1 C`
B. `1 mu C`
C. `0.1C`
D. `0.1 mu C`

Explanation

To find the charge enclosed by the closed surface, we can use Gauss's Law, which relates the electric flux through a closed surface to the charge enclosed by that surface. The formula for Gauss's Law is given by:

\[ \Phi_E = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]

Where:
- \(\Phi_E\) is the electric flux through the closed surface,
- \(Q_{\text{enclosed}}\) is the charge enclosed within the surface,
- \(\epsilon_0\) is the permittivity of free space, approximately \(8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2\).

### Step 1: Calculate the electric flux
Given that the number of electric lines of force radiating from the closed surface is \(1.13 \times 10^{11}\), we can directly use this value as the electric flux (\(\Phi_E\)).

\[ \Phi_E = 1.13 \times 10^{11} \, \text{N m}^2/\text{C} \]

### Step 2: Use Gauss's Law to find the charge enclosed
Rearranging Gauss's Law to solve for \(Q_{\text{enclosed}}\):

\[ Q_{\text{enclosed}} = \Phi_E \cdot \epsilon_0 \]

### Step 3: Substitute the values
Now substituting the values into the equation:

\[ Q_{\text{enclosed}} = (1.13 \times 10^{11}) \cdot (8.85 \times 10^{-12}) \]

### Step 4: Perform the multiplication
Calculating the above expression:

\[ Q_{\text{enclosed}} = 1.13 \times 8.85 \times 10^{11} \times 10^{-12} \]

Calculating \(1.13 \times 8.85\):

\[ 1.13 \times 8.85 \approx 10.00255 \]

Thus:

\[ Q_{\text{enclosed}} \approx 10.00255 \times 10^{-1} \, \text{C} \]

This simplifies to:

\[ Q_{\text{enclosed}} \approx 1.00 \, \text{C} \]

### Final Answer:
The charge enclosed by the surface is approximately \(1.00 \, \text{C}\).

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