Which of the following statements is not true about Gauss's law?

Options

A. Gauss's law is true for any closed surface.
B. The term q on the ringht side of Gauss's law includes the sum of all charges enclosed by the surface.
C. Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry.
D. Gauss's law is based on the inverse square dependence on distance contained in the coulomb's law.

Explanation

To determine which statement is not true about Gauss's law, we will analyze each of the given options step by step.

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

### Step 2: Analyzing Each Statement
1. **Option A**: "Gauss's law is true for any closed surface."
- This statement is true. Gauss's law applies to any closed surface, regardless of its shape.

2. **Option B**: "The term Q on the right-hand side of Gauss's law includes sum of all charges enclosed by the surface."
- This statement is also true. The charge \( Q \) represents the total charge enclosed by the closed surface, which is the sum of all individual charges inside it.

3. **Option C**: "Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry."
- This statement is false. In fact, Gauss's law is particularly useful in systems with symmetry (spherical, cylindrical, planar) because it simplifies the calculation of electric fields.

4. **Option D**: "Gauss's law is based on the inverse square dependence on distance contained in Coulomb's law."
- This statement is true. Gauss's law is derived from Coulomb's law, which shows that the electric force between two point charges decreases with the square of the distance between them.

### Step 3: Conclusion
From the analysis, the statement that is not true about Gauss's law is **Option C**: "Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry."