If the net electric flux through a closed surface is zero, then we can infer :

Options

A. no net charge is enclosed by the surface
B. uniform electric field exists within the surface
C. electric potential varies from point to point inside the surface
D. charge is present inside the surface

Answer

To solve the question, "If the net electric flux through a closed surface is zero, then we can infer:", we will analyze the implications of having zero net electric flux through a closed surface based on Gauss's Law.

### Step-by-Step Solution:

1. **Understanding 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, taking into account the angle (θ) between the electric field and the normal to the surface. Mathematically, it is given by:
\[ Φ = E \cdot A \cdot \cos(θ) \]

2. **Applying Gauss's Law**:
According to Gauss's Law, the net electric flux through a closed surface is proportional to the net charge (Q) enclosed within that surface:
\[ Φ = \frac{Q_{\text{enc}}}{ε_0} \]
where \(ε_0\) is the permittivity of free space.

3. **Analyzing Zero Electric Flux**:
If the net electric flux through the closed surface is zero (Φ = 0), applying Gauss's Law gives:
\[ 0 = \frac{Q_{\text{enc}}}{ε_0} \]
This implies that the net charge enclosed by the surface \(Q_{\text{enc}}\) must be zero:
\[ Q_{\text{enc}} = 0 \]

4. **Conclusion**:
From the above analysis, we can conclude that if the net electric flux through a closed surface is zero, it indicates that there is no net charge enclosed by that surface. Therefore, the correct inference is:
- **No net charge is enclosed by the surface.**

### Evaluation of Other Options:
- **Option 2**: "Uniform electric field exists within the surface" - This is incorrect because a uniform electric field would typically result in a non-zero flux unless the surface is oriented in such a way that the field lines enter and exit equally.

- **Option 3**: "Electric potential varies from point to point inside the surface" - This is also incorrect, as a conductor in electrostatic equilibrium would have a constant potential if there were no net charge inside.

- **Option 4**: "Charge is present inside the surface" - This is incorrect because if there were any charge present, the net flux could not be zero.

### Final Answer:
The correct inference is:
- **No net charge is enclosed by the surface.**