A magnet of magnetic moment M amd pole strenth m is divided in two equal parts, then magnetic moment of each part will be

Explanation

To solve the problem, we need to understand how the magnetic moment of a magnet changes when it is divided into two equal parts.

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment (M) of a magnet is defined as the product of its pole strength (m) and its length (L). Mathematically, this is expressed as:
\[ M = m \cdot L \]

2. **Dividing the Magnet**:
When the magnet is divided into two equal parts, we can consider two cases: dividing it along the horizontal axis and dividing it along the vertical axis.

3. **Case 1 - Horizontal Division**:
- When the magnet is divided horizontally, each part retains the same pole strength (m) but the length of each part becomes half (L/2).
- Therefore, the magnetic moment of each part after horizontal division is:
\[ M_1 = m \cdot \frac{L}{2} = \frac{M}{2} \]

4. **Case 2 - Vertical Division**:
- When the magnet is divided vertically, the length of each part remains the same (L), but the pole strength of each part becomes half (m/2).
- Therefore, the magnetic moment of each part after vertical division is:
\[ M_2 = \frac{m}{2} \cdot L = \frac{M}{2} \]

5. **Conclusion**:
In both cases, whether the magnet is divided horizontally or vertically, the magnetic moment of each part becomes:
\[ M' = \frac{M}{2} \]

Thus, the magnetic moment of each part after dividing the magnet into two equal parts is \( \frac{M}{2} \).