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 assertion and reason question, we need to analyze both statements carefully.

### Step 1: Analyze the Assertion
The assertion states: "In any magnetic field region, the line integral \( \oint \vec{B} \cdot d\vec{l} \) along a closed loop is always zero."

- 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 total current \( I \) 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 the line integral is indeed zero. However, if there is a current enclosed, the integral will not be zero.
- Therefore, the assertion is **false** because it claims that the integral is always zero, which is not true in the presence of enclosed current.

### Step 2: Analyze the Reason
The reason states: "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 also misleading. While the magnetic field \( \vec{B} \) at a point can be influenced by currents enclosed by the loop, it can also be influenced by currents outside the loop or external magnetic fields.
- Therefore, the reason is also **false** because it incorrectly limits the source of the magnetic field to only those currents enclosed by the loop.

### Conclusion
Both the assertion and the reason are false. Thus, the correct answer to the question is that both statements are false.

### Final Answer
Both assertion and reason are false.

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