The total flux linked with unit negative charge put in air is

Options

A. `1/(epsilon_(0)) ` out wards
B. `1/(epsilon_(0))` inwards
C. `1/(4 pi epsilon_(0))` outwards
D. `1/(4 pi epsilon_(0))` inwards

Explanation

To find the total electric flux linked with a unit negative charge placed in air, we can use Gauss's Law, which states that the electric flux (Φ) through a closed surface is equal to the charge (Q) enclosed by that surface divided by the permittivity of free space (ε₀).

### Step-by-Step Solution:

1. **Identify the Charge**:
We have a unit negative charge, which means it is -1 coulomb.

2. **Understand Gauss's Law**:
Gauss's Law is given by the formula:
\[ \Phi = \frac{Q_{\text{in}}}{\epsilon_0} \]
where \( \Phi \) is the electric flux, \( Q_{\text{in}} \) is the charge enclosed by the Gaussian surface, and \( \epsilon_0 \) is the permittivity of free space.

3. **Substitute the Charge**:
Since we have a unit negative charge:
\[ Q_{\text{in}} = -1 \, \text{C} \]

4. **Calculate the Flux**:
Plugging the value of \( Q_{\text{in}} \) into Gauss's Law:
\[ \Phi = \frac{-1}{\epsilon_0} \]

5. **Interpret the Result**:
The negative sign indicates that the direction of the electric flux is inward towards the charge, as expected for a negative charge.

6. **Final Answer**:
Therefore, the total electric flux linked with a unit negative charge in air is:
\[ \Phi = -\frac{1}{\epsilon_0} \]