Gauss’s law states that

Options

A. the total electric flux through a closed surface is `(1)/(epsilon_(0))` times total charge placed near the closed surface .
B. the total electric flux thorought a colsed surface is `(1)/(epsilon_(0))` times the total charge enclosed by the closed surface
C. the total electric flux through an open surface is `(1)/(epsilon_(0))` time the total charge placed near the open surface.
D. the line integral of electric field around the boundary of an open surface is `(1)/(epsilon_(0))` times the total charge placed near the open surface.

Explanation

To solve the question regarding Gauss's law, we will break down the law into its components and analyze the statements provided.

### Step-by-Step Solution:

1. **Understanding Gauss's Law**:
Gauss's law states that the electric flux (Φ_E) through a closed surface is directly proportional to the total charge (Q_enc) enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

2. **Identifying the Key Components**:
- **Electric Flux (Φ_E)**: This is defined as the integral of the electric field (E) over a closed surface (S):
\[ \Phi_E = \oint_S \mathbf{E} \cdot d\mathbf{A} \]
where \( d\mathbf{A} \) is the differential area vector on the surface.

3. **Closed Surface vs. Open Surface**:
- Gauss's law applies to closed surfaces. The concept of electric flux through an open surface does not relate directly to the total charge enclosed.
- Any statement regarding the electric flux through an open surface and the charge "near" that surface is incorrect in the context of Gauss's law.

4. **Correct Statement**:
- The correct interpretation of Gauss's law is that the total electric flux through a closed surface is equal to the charge enclosed divided by \( \epsilon_0 \). Therefore, any statement that suggests the total electric flux through a closed surface is equal to the charge "near" the surface is incorrect.

5. **Conclusion**:
- The correct statement regarding Gauss's law is that the total electric flux through a closed surface is equal to the total charge enclosed divided by \( \epsilon_0 \).

### Final Answer:
Gauss's law states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by \( \epsilon_0 \).

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