If a bar magnet is cut in half, then new magnetic moment m and pole strength M will be:

Options

A. `m, M.`
B. `(m)/(2), M`
C. `(m)/(2), (M)/(2)`
D. `(m)/(4), 2M`

Explanation

To solve the problem of what happens to the magnetic moment (m) and pole strength (M) when a bar magnet is cut in half, we can follow these steps:

### Step 1: Understand the Definitions
- **Magnetic Moment (m)**: The magnetic moment 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.
- **Pole Strength (M)**: The pole strength of a magnet is a measure of the strength of its magnetic poles.

### Step 2: Analyze the Effect of Cutting the Magnet
When a bar magnet is cut in half:
- The length of each half becomes \( \frac{L}{2} \).
- The pole strength \( M \) does not change because each half still retains the same magnetic poles (north and south).

### Step 3: Calculate the New Magnetic Moment
Using the formula for magnetic moment:
- For the original magnet, \( m = M \cdot 2L \).
- For each half, the new length is \( \frac{L}{2} \), so the new magnetic moment \( m' \) for each half becomes:
\[ m' = M \cdot 2 \left(\frac{L}{2}\right) = M \cdot L \]
- Thus, the new magnetic moment \( m' \) is half of the original magnetic moment \( m \).

### Step 4: Conclusion
- The new magnetic moment \( m' \) after cutting the magnet in half is \( \frac{m}{2} \).
- The pole strength \( M \) remains unchanged.

### Final Answer:
- New magnetic moment \( m' = \frac{m}{2} \)
- Pole strength \( M \) remains the same.

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