which of the following statement is correct?

Options

A. electric field calculated by gauss law is the the field due to only those charges which are enclosed inside the Gaussian surface
B. gauss law is applicable only when there is a symmetrical distribution of charge
C. electric flux through a closed surface is equal to total flux due to all the charge enclosed with in that surface only
D. all of this

Answer

To determine which of the given statements is correct, we will analyze each statement one by one based on the principles of Gauss's law.

### Step-by-Step Solution:

1. **Analyzing Statement 1:**
- Statement: "Electric field calculated by Gauss's law is the field due to only those charges which are enclosed inside the Gaussian surface."
- According to Gauss's law, the electric flux through a closed surface is proportional to the charge enclosed within that surface. However, the electric field at a point outside the Gaussian surface is influenced by both the enclosed charges and any external charges. Therefore, this statement is **incorrect**.

**Hint:** Remember that the electric field outside a Gaussian surface is influenced by both enclosed and external charges.

2. **Analyzing Statement 2:**
- Statement: "Gauss's law is applicable only when there is a symmetrical distribution of charge."
- Gauss's law can be applied to any closed surface regardless of the symmetry of the charge distribution. While symmetrical distributions make calculations easier, Gauss's law is valid in all scenarios. Thus, this statement is also **incorrect**.

**Hint:** Gauss's law is universal and does not depend on the symmetry of charge distribution.

3. **Analyzing Statement 3:**
- Statement: "Electric flux through the closed surface is equal to total flux due to all charges enclosed within that surface only."
- This statement is consistent with Gauss's law, which states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀). Therefore, this statement is **correct**.

**Hint:** Recall that Gauss's law relates electric flux directly to the enclosed charge.

4. **Analyzing Statement 4:**
- Since we have already determined that the first three statements are incorrect or correct, we can conclude that the fourth statement must be incorrect if it contradicts the correct statement we found.

### Conclusion:
- The correct statement is **Statement 3**: "Electric flux through the closed surface is equal to total flux due to all charges enclosed within that surface only."