A: In any magnetic field region the line integral `ointvecB.vec(dl)` along a closed loop is always zero.
R: The magnetic field `vecB` in the expressioin `oint vecB.vec(dl)` is due to the currents enclosed only by the loop.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark 2.
C. If assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the given problem, we need to analyze both the assertion (A) and the reason (R) statements regarding the line integral of the magnetic field \( \vec{B} \) along a closed loop.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the line integral \( \oint \vec{B} \cdot d\vec{l} \) along a closed loop is always zero in any magnetic field region.
- This assertion is based on the application of Ampere's Circuital Law, which relates the magnetic field around a closed loop to the current enclosed by that loop.

2. **Applying Ampere's Circuital Law**:
- According to Ampere's Circuital Law, the line integral of the magnetic field \( \vec{B} \) around a closed loop is equal to the permeability of free space \( \mu_0 \) times the net current \( I_{\text{enc}} \) enclosed by the loop:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}} \]
- If there is no current enclosed by the loop (\( I_{\text{enc}} = 0 \)), then:
\[ \oint \vec{B} \cdot d\vec{l} = 0 \]
- However, if there is current enclosed, the integral will not be zero.

3. **Evaluating the Assertion**:
- Since the assertion claims that the integral is always zero, it is incorrect because it depends on whether there is current enclosed by the loop or not.

4. **Understanding the Reason (R)**:
- The reason states that the magnetic field \( \vec{B} \) in the expression \( \oint \vec{B} \cdot d\vec{l} \) is due to the currents enclosed only by the loop.
- This statement is true as per Ampere's Circuital Law, which specifies that the magnetic field around a closed loop is determined by the current that is enclosed by that loop.

5. **Conclusion**:
- The assertion (A) is false because the line integral \( \oint \vec{B} \cdot d\vec{l} \) is not always zero; it is zero only when there is no current enclosed.
- The reason (R) is true because it accurately describes the relationship between the magnetic field and the enclosed current.

### Final Answer:
- Assertion (A) is false.
- Reason (R) is true.