If a magnet of pole strength m is divided into four parts such that the length and width of each part is half that of initial one, then the pole strength of each part will be

Options

A. `m//4`
B. `m//2`
C. `m//8`
D. `4m`

Explanation

To solve the problem, we need to understand how the pole strength of a magnet behaves when it is divided into smaller parts.

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the initial magnet have a pole strength \( M \).
- The magnet is divided into 4 parts, and each part has a length and width that is half of the original magnet.

2. **Determine the Volume of the Original Magnet**:
- Let the original dimensions of the magnet be \( L \) (length), \( W \) (width), and \( H \) (height).
- The volume of the original magnet \( V = L \times W \times H \).

3. **Determine the Dimensions of Each Part**:
- When the magnet is divided into 4 parts, the new dimensions of each part will be:
- Length \( = \frac{L}{2} \)
- Width \( = \frac{W}{2} \)
- Height \( = H \) (assuming height remains the same for simplicity).
- Therefore, the volume of each part \( V' = \left(\frac{L}{2}\right) \times \left(\frac{W}{2}\right) \times H = \frac{L \times W \times H}{4} = \frac{V}{4} \).

4. **Pole Strength of Each Part**:
- The pole strength \( p \) of a magnet is defined as the product of the pole strength of the magnet and the volume of the magnet.
- Since the total pole strength of the original magnet is \( M \), we can express the pole strength of each part as:
\[ p' = \frac{M}{4} \]
- This is because the pole strength is distributed evenly among the four parts, and since each part has a volume that is a quarter of the original, the pole strength will also be a quarter.

5. **Conclusion**:
- Therefore, the pole strength of each part after dividing the original magnet into four smaller parts is:
\[ p' = \frac{M}{4} \]

### Final Answer:
The pole strength of each part will be \( \frac{M}{4} \).