Out of two magnets of same length and ole strength, one has a small hole at the centre. Then:

Options

A. One with hole has small magnetic moment
B. One with hole has large magnetic moment
C. both have equal magnetic moment
D. Magnetic moment is independent of pole strength

Explanation

To solve the problem, we need to analyze the effect of having a hole in one of the two magnets of the same length and pole strength.

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment (M) of a magnet is given by the formula:
\[ M = m \cdot 2l \]
where \( m \) is the pole strength and \( l \) is the length of the magnet.

2. **Identifying the Magnets**:
We have two magnets:
- Magnet A: No hole
- Magnet B: Has a small hole at the center

3. **Effect of the Hole**:
The presence of a hole in Magnet B will effectively reduce its length. This is because the hole removes a portion of the material that contributes to the magnetic moment.

4. **Calculating Effective Length**:
For Magnet B, the effective length can be considered as:
\[ l' = l - \text{(length of the hole)} \]
Since the hole is at the center, it reduces the effective length of Magnet B.

5. **Calculating Magnetic Moment for Both Magnets**:
- For Magnet A (without a hole):
\[ M_A = m \cdot 2l \]
- For Magnet B (with a hole):
\[ M_B = m \cdot 2l' = m \cdot 2(l - \text{(length of the hole)}) \]

6. **Comparing Magnetic Moments**:
Since \( l' < l \), it follows that:
\[ M_B < M_A \]
Therefore, the magnet with the hole (Magnet B) has a smaller magnetic moment compared to the magnet without the hole (Magnet A).

7. **Conclusion**:
The magnet with the hole has a smaller magnetic moment than the one without the hole.

### Final Answer:
The magnet with the hole has a smaller magnetic moment compared to the magnet without a hole.

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