A bar magnet of moment M and pole strength m is cut into parts of equal lengths. The magetic moment and pole strength of either part is

Options

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

Explanation

To solve the problem of a bar magnet being cut into equal lengths and determining the magnetic moment and pole strength of each part, we can follow these steps:

### Step 1: Understand the Definitions
- **Magnetic Moment (M)**: The magnetic moment of a bar magnet is defined as the product of its pole strength (m) and the length (l) of the magnet. Mathematically, it is given by:
\[ M = m \cdot l \]

### Step 2: Cutting the Magnet
- When the bar magnet is cut into equal lengths, let's assume it is cut into \( n \) parts. If the original length of the magnet is \( l \), then the length of each part after cutting will be:
\[ l' = \frac{l}{n} \]

### Step 3: Pole Strength
- The pole strength \( m \) of a magnet does not change when the magnet is cut. Therefore, for each part, the pole strength remains:
\[ m' = m \]

### Step 4: Magnetic Moment of Each Part
- The magnetic moment \( M' \) of each part can be calculated using the formula for magnetic moment:
\[ M' = m' \cdot l' = m \cdot \frac{l}{n} \]
- Since the original magnetic moment \( M \) is \( M = m \cdot l \), we can express \( M' \) as:
\[ M' = \frac{M}{n} \]

### Step 5: Conclusion
- Therefore, after cutting the magnet into \( n \) equal parts:
- The pole strength of each part remains \( m \).
- The magnetic moment of each part becomes \( \frac{M}{n} \).

### Final Answer
- The magnetic moment of either part is \( \frac{M}{n} \) and the pole strength remains \( m \).

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