If two bar magnets of different magnetic lengths have equal moments, then the pole strength is

Options

A. equal for both the magnets
B. less for shorter magnet
C. more for shorter magnet
D. more fore longer magnet

Answer

To solve the problem, we need to understand the relationship between the magnetic moment, pole strength, and the magnetic length of the bar magnets.

### Step-by-Step Solution:

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

2. **Given Condition**:
We have two bar magnets with different magnetic lengths but equal magnetic moments. Let's denote the pole strengths and lengths of the two magnets as follows:
- For the first magnet: \( M_1 = p_1 \cdot l_1 \)
- For the second magnet: \( M_2 = p_2 \cdot l_2 \)

Since the moments are equal, we can write:
\[ p_1 \cdot l_1 = p_2 \cdot l_2 \]

3. **Rearranging the Equation**:
From the equality of moments, we can express the pole strength in terms of the lengths:
\[ \frac{p_1}{p_2} = \frac{l_2}{l_1} \]

4. **Understanding the Implication**:
If \( l_1 \) is less than \( l_2 \) (i.e., the first magnet is shorter), then \( \frac{l_2}{l_1} > 1 \). This implies that:
\[ p_1 > p_2 \]
Conversely, if \( l_1 \) is greater than \( l_2 \) (i.e., the first magnet is longer), then \( \frac{l_2}{l_1} < 1 \), which implies:
\[ p_1 < p_2 \]

5. **Conclusion**:
Since the two magnets have equal moments, the magnet with the shorter length must have a greater pole strength. Thus, if one magnet is shorter, its pole strength is higher compared to the longer magnet.

### Final Answer:
If two bar magnets of different magnetic lengths have equal moments, then the pole strength of the shorter magnet is greater than that of the longer magnet.

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