A bar magnet of magnetic moment 80 units is cut into two halves of equal length, the magnetic moment of each half will be:

Options

A. 80 units
B. 40 units
C. 60 units
D. 20 units

Answer

To find the magnetic moment of each half of a bar magnet when it is cut into two equal parts, we can follow these steps:

### Step-by-Step Solution:

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

2. **Initial Magnetic Moment**: The initial magnetic moment of the bar magnet is given as 80 units. Therefore, we can write:
\[ M = 80 \text{ units} \]

3. **Cutting the Magnet**: When the bar magnet is cut into two equal halves, each half will have:
- The same pole strength \( m \) as the original magnet.
- A new length \( L' = \frac{L}{2} \) (since it is cut into two equal parts).

4. **Magnetic Moment of Each Half**: The magnetic moment of each half (let's denote it as \( M' \)) can be expressed as:
\[ M' = m \cdot L' = m \cdot \left(\frac{L}{2}\right) \]

5. **Relating the Moments**: Since the original magnetic moment \( M \) is \( m \cdot L \), we can relate the magnetic moment of each half to the original:
\[ M' = m \cdot \left(\frac{L}{2}\right) = \frac{m \cdot L}{2} = \frac{M}{2} \]

6. **Calculating the New Magnetic Moment**: Substituting the value of \( M \):
\[ M' = \frac{80 \text{ units}}{2} = 40 \text{ units} \]

7. **Conclusion**: Therefore, the magnetic moment of each half of the bar magnet is:
\[ \text{Magnetic moment of each half} = 40 \text{ units} \]

### Final Answer:
The magnetic moment of each half will be **40 units**.

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