Total electric flux coming out of a unit positive charge put in air is

Options

A. `epsilon_(0)`
B. `(1)/(epsilon_(0))`
C. `(1)/(4pi epsilon_(0))`
D. `4pi epsilon_(0)`

Answer

To solve the question regarding the total electric flux coming out of a unit positive charge placed in air, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electric Flux**:
Electric flux (Φ) through a surface is defined as the product of the electric field (E) and the area (A) through which the field lines pass, mathematically expressed as:
\[ \Phi = E \cdot A \]
However, we will use Gauss's Law for this problem.

2. **Identify the Charge and Gaussian Surface**:
We have a unit positive charge, which means \( q = +1 \, \text{C} \). We will consider a Gaussian surface that encloses this charge. A common choice is a spherical surface centered around the charge.

3. **Apply Gauss's Law**:
Gauss's Law states that the total electric flux through a closed surface is equal to the charge enclosed (Q_enc) divided by the permittivity of free space (ε₀):
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]

4. **Determine the Charge Enclosed**:
Since we have placed a unit positive charge inside the Gaussian surface, the charge enclosed \( Q_{\text{enc}} = +1 \, \text{C} \).

5. **Calculate the Electric Flux**:
Substituting the charge enclosed into Gauss's Law, we get:
\[ \Phi = \frac{1}{\epsilon_0} \]

6. **Conclusion**:
Therefore, the total electric flux coming out of a unit positive charge placed in air is:
\[ \Phi = \frac{1}{\epsilon_0} \]

### Final Answer:
The total electric flux coming out of a unit positive charge put in air is \( \frac{1}{\epsilon_0} \).