Given below are two statements labelled as Assertion (A) and Reason ( R)
Assertion (A )Total flux through a closed surface is zero if no charge in enclosed by the surface.
Reason (R ): Gauss law is true for any closed surface , no matter what its shape or size is.

Options

A. Both A and R are true and R is also the correct explanation of A.
B. Both A and R are true but R is not the correct explanation of A .
C. A is true but R is false.
D. A is false and R is also false.

Answer

To solve the given question, we need to analyze the Assertion (A) and Reason (R) statements regarding Gauss's Law.

### Step-by-Step Solution:

**Step 1: Analyze the Assertion (A)**
The assertion states: "Total flux through a closed surface is zero if no charge is enclosed by the surface."
According to Gauss's Law, the electric flux (Φ) through a closed surface is given by the equation:
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]
where \( Q_{\text{enc}} \) is the total charge enclosed within the surface and \( \epsilon_0 \) is the permittivity of free space.
If there is no charge enclosed by the surface, \( Q_{\text{enc}} = 0 \). Therefore, the total flux through the surface becomes:
\[ \Phi = \frac{0}{\epsilon_0} = 0 \]
Thus, the assertion is **true**.

**Step 2: Analyze the Reason (R)**
The reason states: "Gauss law is true for any closed surface, no matter what its shape or size is."
Gauss's Law indeed applies to any closed surface, regardless of its shape or size. The law holds as long as the surface is closed. Therefore, the reason is also **true**.

**Step 3: Determine the Relationship Between A and R**
While both statements are true, the reason does not serve as an explanation for the assertion. The assertion specifically addresses the condition of zero enclosed charge leading to zero flux, while the reason discusses the applicability of Gauss's Law to any closed surface. Thus, the reason does not explain why the total flux is zero when no charge is enclosed.

**Conclusion**:
Both the assertion and reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is that Assertion (A) is true, Reason (R) is true, but R is not the correct explanation of A.

### Final Answer:
Assertion (A) is true, Reason (R) is true, but R is not the correct explanation of A.

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