The ratio of pole strength of two pieces of a large magnet when it is broken such that ratio of their length is 4:1 is:

Options

A. `2:1`
B. `1:2`
C. `4:1`
D. `3:1`

Explanation

To solve the problem of finding the ratio of pole strength of two pieces of a large magnet when it is broken such that the ratio of their lengths is 4:1, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Pole Strength**:
- Pole strength (denoted as 'm') is a measure of the strength of the magnetic poles of a magnet. It is defined as the product of the magnetic field strength and the length of the magnet.

2. **Breaking the Magnet**:
- When a magnet is broken, each piece retains its pole strength. The pole strength of a magnet is not dependent on its length but rather on the material and the total magnetic moment.

3. **Ratio of Lengths**:
- Given that the lengths of the two pieces are in the ratio of 4:1, let’s denote the lengths of the two pieces as L1 and L2, where L1 = 4x and L2 = x for some length x.

4. **Pole Strength Calculation**:
- The pole strength of a magnet is given by the formula:
\[ m = \frac{M}{L} \]
where M is the magnetic moment and L is the length of the magnet.
- Since the total magnetic moment (M) of the entire magnet remains constant when it is broken, the pole strength of each piece will depend on its length.

5. **Finding the Ratio of Pole Strengths**:
- For the first piece (length L1 = 4x):
\[ m_1 = \frac{M}{L_1} = \frac{M}{4x} \]
- For the second piece (length L2 = x):
\[ m_2 = \frac{M}{L_2} = \frac{M}{x} \]

6. **Calculating the Ratio**:
- The ratio of the pole strengths \( m_1 \) and \( m_2 \) is:
\[ \frac{m_1}{m_2} = \frac{\frac{M}{4x}}{\frac{M}{x}} = \frac{1}{4} \]

7. **Conclusion**:
- Therefore, the ratio of the pole strength of the two pieces of the magnet is \( 1:4 \).

### Final Answer:
The ratio of pole strength of the two pieces of the magnet when it is broken is \( 1:4 \).

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