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 the properties of electric flux and Gauss's law step by step.

### Step-by-Step Solution:

1. **Understanding Gauss's Law**:
Gauss's law states that the total electric flux (Φ) through a closed surface (Gaussian surface) is proportional to the net charge (Q_enclosed) enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]
where ε₀ is the permittivity of free space.

**Hint**: Recall that Gauss's law relates electric flux to the enclosed charge and is fundamental in electrostatics.

2. **Dependence on Enclosed Charge**:
From Gauss's law, we see that the electric flux through the Gaussian surface depends directly on the amount of charge enclosed. If the enclosed charge increases, the electric flux increases proportionally.

**Hint**: Consider how the electric field lines relate to the amount of charge; more charge means more field lines and thus more flux.

3. **Nature of Electric Flux**:
Electric flux is a scalar quantity. This is because it is derived from the dot product of the electric field vector and the area vector of the surface, which results in a scalar value.

**Hint**: Remember that scalar quantities have magnitude but no direction, unlike vector quantities.

4. **Independence from Shape of Gaussian Surface**:
The electric flux through a Gaussian surface is independent of the shape of that surface. As long as the charge enclosed remains the same, the flux will remain constant regardless of how the surface is shaped.

**Hint**: Think about how the same charge can be surrounded by different shapes (like a sphere, cube, etc.) but still produces the same amount of electric field lines passing through.

5. **Conclusion**:
Based on the above analysis:
- Statement 1: True (depends on the magnitude of charge enclosed)
- Statement 2: True (electric flux is a scalar quantity)
- Statement 3: True (electric flux is independent of the shape of the Gaussian surface)
- Statement 4: True (all previous statements are true)

Therefore, the correct answer is that all statements are true.

**Final Answer**: All are true (Option 4).