Statement I: no electric current will be present within a region having uniform and constant magetic field.
Statement II: Within a region of unifrom and cinstant magnetic field `vec(B)`, the path integral of magnetic field `oint vec(B).dvec(l)` along any closed path is zero. Hence, from Ampere cirauital law `oint vec(B).dvec(l) = mu_(0)I` (where the given terms ahve usual meaning), no current can be present within a region having uniform and constant magnetic field .

Options

A. (a) Statement I is True, Statement II is True, Statement II is correct expaination for Statement I.
B. (b) Statement I is True, Statement II is True, Statement II is NOT a correct expaination for Statement I.
C. ( c) Statement I is True, Statement II is false.
D. ( d) Statement I is False, Statement II is True.

Explanation

To solve the given question, we need to analyze both statements and determine their validity based on the principles of electromagnetic induction and Ampere's circuital law.

### Step-by-step Solution:

1. **Understanding Statement I**:
- Statement I claims that "no electric current will be present within a region having a uniform and constant magnetic field."
- According to Ampere's circuital law, the line integral of the magnetic field \( \oint \vec{B} \cdot d\vec{l} \) around a closed loop is related to the current \( I \) passing through that loop by the equation:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I \]
- If the magnetic field \( \vec{B} \) is uniform and constant, the line integral \( \oint \vec{B} \cdot d\vec{l} \) will be zero because there is no net change in the magnetic field along a closed path.

2. **Analyzing Statement II**:
- Statement II states that "within a region of uniform and constant magnetic field \( \vec{B} \), the path integral \( \oint \vec{B} \cdot d\vec{l} \) along any closed path is zero."
- This is indeed true as per the properties of a uniform magnetic field. Since the magnetic field does not change in magnitude or direction, the integral evaluates to zero.

3. **Connecting the Statements**:
- Since \( \oint \vec{B} \cdot d\vec{l} = 0 \) implies \( \mu_0 I = 0 \), it follows that \( I = 0 \) when \( \vec{B} \) is uniform and constant.
- Therefore, Statement I is true because it logically follows from Statement II.

4. **Conclusion**:
- Both statements are true, and Statement II provides a correct explanation for Statement I.
- Therefore, the correct option is that both statements are true, and Statement II is a correct explanation for Statement I.

### Final Answer:
- Both Statement I and Statement II are true, and Statement II is a correct explanation for Statement I. The correct option is **A**.