Which statement is true for Gauss law-

Options

A. All the charges whether inside or outside the gaussian surface contribute to the electric flux.
B. Electric flux depends upon the geometry of the gaussian surface.
C. Gauss theorem can be applied to non-uniform electric field
D. The electric field over the gaussian surface remains continuous and uniform at every point

Answer

To determine which statement is true regarding Gauss's Law, let's analyze each of the provided options step-by-step:

### Step 1: Understanding Gauss's Law
Gauss's Law states that the electric flux (Φ) through a closed surface is proportional to the total charge (Q) enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi = \frac{Q_{\text{in}}}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

### Step 2: Analyzing Each Statement

1. **Statement 1**: "All the charges, whether inside or outside the Gaussian surface, contribute to the electric flux."
- **Analysis**: This statement is **false**. Only the charges inside the Gaussian surface contribute to the electric flux. Charges outside do not affect the flux through the surface.

2. **Statement 2**: "Electric flux depends upon the geometry of the Gaussian surface."
- **Analysis**: This statement is also **false**. The electric flux through a Gaussian surface depends solely on the charge enclosed and not on the shape or size of the surface.

3. **Statement 3**: "Gauss's theorem can be applied to non-uniform electric fields."
- **Analysis**: This statement is **misleading**. While Gauss's Law can technically be applied in non-uniform fields, it is most useful and straightforward in uniform electric fields. Therefore, this statement is generally considered **false** in the context of basic applications.

4. **Statement 4**: "The electric field over a Gaussian surface remains continuous and uniform at every point."
- **Analysis**: This statement is **true**. In a uniform electric field, the electric field is constant in magnitude and direction across the Gaussian surface. Even in non-uniform fields, the electric field is continuous across the surface.

### Conclusion
Based on the analysis, the **correct statement** regarding Gauss's Law is **Statement 4**.

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