Flux coming out from a positive unit charge placed in air, is

Options

A. `epsi_(0)`
B. `epsi_(0)^(-1)`
C. `(4 pi epsi_(0))^(-1)`
D. `4 pi epsi_(0)`

Answer

To find the electric flux coming out from a positive unit charge placed in air, we can use Gauss's law. Here’s a step-by-step solution:

### Step 1: Understand Gauss's Law
Gauss's law 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). Mathematically, this is expressed as:
\[ Φ = \frac{Q}{ε₀} \]

### Step 2: Identify the Charge
In this case, we have a positive unit charge. A unit charge is defined as 1 coulomb. Therefore, we have:
\[ Q = +1 \, \text{C} \]

### Step 3: Use the Value of Permittivity
The permittivity of free space (ε₀) is a constant value approximately equal to:
\[ ε₀ ≈ 8.85 \times 10^{-12} \, \text{C}^2/\text{N·m}^2 \]

### Step 4: Calculate the Electric Flux
Substituting the values of Q and ε₀ into Gauss's law, we get:
\[ Φ = \frac{Q}{ε₀} = \frac{1 \, \text{C}}{ε₀} \]
Thus, the electric flux coming out from the positive unit charge is:
\[ Φ = \frac{1}{ε₀} \]

### Step 5: Conclusion
The electric flux coming out from a positive unit charge placed in air is given by:
\[ Φ = \frac{1}{ε₀} \]
This indicates that the flux is inversely proportional to the permittivity of free space.