Assertion:- In a given situation of arrangement of charges, an extra charge is placed outside the Gaussion surface. In the Gauss Theroem
`ointvecEdvecs=(Q_(in))/(epsilon_(0))Q_(in)` remains unchanged whereas electric field `vecE` at the site of the element is changed.
Reason:- Electric field `vecE` at any point on the Gaussian surface is due to inside charge only.

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Explanation

To solve the question, we need to analyze the assertion and the reason provided in the context of Gauss's law.

### Step-by-Step Solution:

1. **Understanding Gauss's Law**: Gauss's law states that the electric flux through a closed surface (Gaussian surface) is proportional to the charge enclosed within that surface. Mathematically, it is expressed as:
\[ \oint \vec{E} \cdot d\vec{s} = \frac{Q_{\text{in}}}{\epsilon_0} \]
where \( \oint \vec{E} \cdot d\vec{s} \) is the total electric flux through the surface, \( Q_{\text{in}} \) is the charge enclosed by the surface, and \( \epsilon_0 \) is the permittivity of free space.

2. **Analyzing the Assertion**: The assertion states that when an extra charge is placed outside the Gaussian surface, the total enclosed charge \( Q_{\text{in}} \) remains unchanged. This is true because the charge outside the Gaussian surface does not contribute to the enclosed charge. Therefore, the left-hand side of Gauss's law remains equal to \( \frac{Q_{\text{in}}}{\epsilon_0} \).

3. **Electric Field Change**: The assertion also mentions that the electric field \( \vec{E} \) at the site of the element is changed. This is true because the presence of an external charge can influence the electric field at points on the Gaussian surface, even though it does not change the total enclosed charge.

4. **Analyzing the Reason**: The reason provided states that the electric field \( \vec{E} \) at any point on the Gaussian surface is due to the inside charge only. This is incorrect because while the enclosed charge determines the total flux, the electric field at any point on the surface can also be influenced by external charges. Therefore, the reason is false.

5. **Conclusion**: The assertion is true, but the reason is false. Thus, the correct answer to the question is that the assertion is true, and the reason is false.

### Final Answer:
- **Assertion**: True
- **Reason**: False