What will be the total flux coming out of a unit positive charge put in air?

Options

A. 0
B. `epsi_(0)^(-1)`
C. 1
D. `epsi_(0)^(-2)`

Explanation

To find the total electric flux coming out of a unit positive charge placed in air, we can use Gauss's Law. According to Gauss's Law, the electric flux (Φ) through a closed surface is proportional to the charge (Q) enclosed by that surface. The formula for electric flux is given by:

\[ \Phi = \frac{Q}{\epsilon_0} \]

Where:
- \( \Phi \) is the electric flux,
- \( Q \) is the charge enclosed,
- \( \epsilon_0 \) is the permittivity of free space (approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \)).

### Step-by-Step Solution:

1. **Identify the Charge**: We have a unit positive charge, which means \( Q = 1 \, \text{C} \).

2. **Use Gauss's Law**: According to Gauss's Law, the total electric flux through a closed surface surrounding the charge is given by the equation:
\[ \Phi = \frac{Q}{\epsilon_0} \]

3. **Substitute the Values**: Plugging in the values we have:
\[ \Phi = \frac{1 \, \text{C}}{\epsilon_0} \]

4. **Determine the Value of \( \epsilon_0 \)**: The permittivity of free space \( \epsilon_0 \) is a constant:
\[ \epsilon_0 \approx 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \]

5. **Calculate the Electric Flux**: Therefore, the total electric flux becomes:
\[ \Phi = \frac{1}{8.85 \times 10^{-12}} \, \text{N m}^2/\text{C} \]

6. **Final Result**: The total electric flux coming out of a unit positive charge in air is:
\[ \Phi \approx 1.13 \times 10^{11} \, \text{N m}^2/\text{C} \]