Which of the following is true for electric-flux through a Gaussian surface ?

Options

A. It depends on magnitude of charge enclosed by Gaussian surface
B. Electric flux is scalar quantity
C. Electric flux is independent of shape of Gaussian surface enclosing the charge
D. All are true

Answer

To determine which statements are true regarding electric flux through a Gaussian surface, we can analyze each option based on Gauss's law.

### Step-by-Step Solution:

1. **Understanding Gauss's Law**:
Gauss's law states that the electric flux (Φ) through a closed surface (Gaussian surface) is directly proportional to the charge (Q) enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi = \frac{Q}{\varepsilon_0} \]
where \( \varepsilon_0 \) is the permittivity of free space.

2. **Analyzing Option 1**:
- **Statement**: It depends on the magnitude of charge enclosed by the Gaussian surface.
- **Evaluation**: This statement is true because the electric flux is directly proportional to the charge enclosed. Thus, if the charge changes, the electric flux will also change.

3. **Analyzing Option 2**:
- **Statement**: Electric flux is a scalar quantity.
- **Evaluation**: This statement is also true. The electric flux is calculated using the charge (a scalar) divided by \( \varepsilon_0 \) (a constant), which means the result is a scalar quantity.

4. **Analyzing Option 3**:
- **Statement**: Electric flux is independent of the shape of the Gaussian surface enclosing the charge.
- **Evaluation**: This statement is true as well. According to Gauss's law, the electric flux depends only on the charge enclosed and not on the shape or size of the Gaussian surface.

5. **Conclusion**:
Since all three statements are true, the correct answer is:
- **Option 4**: All are true.

### Final Answer:
The correct choice is **Option 4: All are true**.