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 solve the problem of finding the magnetic moment of each half of a bar magnet when it is cut into two equal halves, we can follow these steps:

### Step-by-Step Solution:

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

2. **Initial Magnetic Moment**: We are given that the initial magnetic moment of the bar magnet is 80 units. Therefore:
\[ M = 80 \text{ units} \]

3. **Cutting the Magnet**: When the bar magnet is cut into two equal halves, each half will have a length of \( \frac{L}{2} \).

4. **Magnetic Moment of Each Half**: The pole strength (m) remains unchanged when the magnet is cut. Therefore, the magnetic moment of each half (M') can be calculated as:
\[ M' = m \cdot \left(\frac{L}{2}\right) \]

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

6. **Calculating the New Magnetic Moment**: Substituting the initial magnetic moment into the equation gives:
\[ M' = \frac{80}{2} = 40 \text{ units} \]

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

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