A: The magnetic moment of a current carrying planar loop does depend on the space of the loop.
R: The magnetic moemnt is a vector quantity.

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 provided:

**Assertion (A):** The magnetic moment of a current-carrying planar loop does depend on the space of the loop.
**Reason (R):** The magnetic moment is a vector quantity.

### Step-by-Step Solution:

1. **Understanding Magnetic Moment:**
- The magnetic moment (M) of a current-carrying loop is defined as the product of the current (I) flowing through the loop and the area (A) of the loop.
- The formula for magnetic moment is given by:
\[ M = I \times A \]

2. **Dependence on Area:**
- The area (A) of the loop is directly related to its dimensions (length and breadth for a rectangular loop, or radius for a circular loop).
- Therefore, if the dimensions of the loop change, the area changes, which in turn affects the magnetic moment.
- For example, for a rectangular loop:
\[ A = \text{length} \times \text{breadth} \]
- For a circular loop:
\[ A = \pi r^2 \]
- Hence, the assertion that the magnetic moment depends on the space (dimensions) of the loop is **true**.

3. **Understanding the Vector Nature of Magnetic Moment:**
- The magnetic moment is indeed a vector quantity. This means it has both magnitude and direction.
- The direction of the magnetic moment is perpendicular to the plane of the loop and follows the right-hand rule.
- The vector nature of magnetic moment arises from its dependence on both the current and the area vector (which has direction).

4. **Evaluating the Reason:**
- The reason states that the magnetic moment is a vector quantity, which is also **true**.
- However, the reason does not explain why the assertion is true. It merely states a property of the magnetic moment without linking it to the dependence on the loop's dimensions.

5. **Conclusion:**
- Both the assertion and reason are true, but the reason does not correctly explain the assertion.
- Therefore, the correct answer is that the assertion is true, and the reason is true but does not provide the correct explanation for the assertion.

### Final Answer:
- **Assertion (A) is true.**
- **Reason (R) is true, but it is not the correct explanation for (A).**
- Thus, the answer is **B**.