A bar magnet of magnetic moment M and pole strength m is broken in two equal part along the magnetic axis . The magnetic moment and pole strength of each part are

Options

A. `(M)/(2) , (m)/(2)`
B. `(M)/(2)` , m
C. `M , (m)/(2)`
D. M , m

Answer

To solve the problem, we need to analyze the properties of the bar magnet before and after it is broken into two equal parts along its magnetic axis.

### Step-by-Step Solution:

1. **Understanding the Initial Magnet**:
- A bar magnet has a magnetic moment \( M \) and pole strength \( m \).
- The length of the bar magnet is denoted as \( l \).
- The magnetic moment \( M \) of the bar magnet is given by the formula:
\[ M = m \cdot l \]

2. **Breaking the Magnet**:
- When the bar magnet is broken into two equal parts along the magnetic axis, each part will have half the length of the original magnet.
- Therefore, the length of each part becomes \( \frac{l}{2} \).

3. **Determining the Pole Strength of Each Part**:
- The pole strength of a magnet is defined as the strength of each pole. When the magnet is broken, the pole strength of each part is halved.
- Thus, the pole strength of each part becomes:
\[ m' = \frac{m}{2} \]

4. **Calculating the Magnetic Moment of Each Part**:
- The magnetic moment \( M' \) of each part can be calculated using the new pole strength and the new length:
\[ M' = m' \cdot \left(\frac{l}{2}\right) \]
- Substituting \( m' = \frac{m}{2} \):
\[ M' = \left(\frac{m}{2}\right) \cdot \left(\frac{l}{2}\right) = \frac{m \cdot l}{4} \]
- Since the original magnetic moment \( M = m \cdot l \), we can express the new magnetic moment as:
\[ M' = \frac{M}{2} \]

5. **Final Results**:
- After breaking the magnet, each part has:
- Pole Strength: \( \frac{m}{2} \)
- Magnetic Moment: \( \frac{M}{2} \)

### Conclusion:
Thus, the magnetic moment and pole strength of each part after breaking the bar magnet are:
- Magnetic Moment: \( \frac{M}{2} \)
- Pole Strength: \( \frac{m}{2} \)