If the electric flux entering and leaving an enclosed surface respectively is `phi_1` and `phi_2`, the electric charge inside the surface will be

Options

A. (a) `(phi_2-phi_1)epsilon_o`
B. (b) `(phi_1+phi_2)//epsilon_o`
C. (c) `(phi_2-phi_1)//epsilon_o`
D. (d) `(phi_1+phi_2)epsilon_o`

Explanation

To find the electric charge inside an enclosed surface when the electric flux entering and leaving the surface are given as \( \phi_1 \) and \( \phi_2 \) respectively, we can use Gauss's law.

### Step-by-Step Solution:

1. **Understand the Concept of Electric Flux:**
Electric flux (\( \Phi \)) through a surface is defined as the product of the electric field (\( E \)) and the area (\( A \)) through which it passes, and it is given by the formula:
\[ \Phi = E \cdot A \]

2. **Apply Gauss's Law:**
According to Gauss's law, the net electric flux (\( \Phi_{\text{net}} \)) through a closed surface is equal to the charge (\( Q \)) enclosed by that surface divided by the permittivity of free space (\( \epsilon_0 \)):
\[ \Phi_{\text{net}} = \frac{Q}{\epsilon_0} \]

3. **Calculate the Net Electric Flux:**
The net electric flux through the surface can be calculated as the difference between the flux leaving the surface (\( \phi_2 \)) and the flux entering the surface (\( \phi_1 \)):
\[ \Phi_{\text{net}} = \phi_2 - \phi_1 \]

4. **Relate the Net Electric Flux to Charge:**
Substituting the expression for net electric flux into Gauss's law gives:
\[ \phi_2 - \phi_1 = \frac{Q}{\epsilon_0} \]

5. **Solve for the Enclosed Charge \( Q \):**
Rearranging the equation to solve for the charge \( Q \) gives:
\[ Q = (\phi_2 - \phi_1) \cdot \epsilon_0 \]

### Final Answer:
Thus, the electric charge inside the surface is:
\[ Q = (\phi_2 - \phi_1) \cdot \epsilon_0 \]