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

Options

A. M
B. `M//2`
C. `M//4`
D. 2M

Answer

To solve the question, we need to analyze the properties of a magnet when it is divided into two equal parts. The magnetic moment (M) and pole strength (m) of the original magnet are given, and we want to find the magnetic moment of each part after division.

### Step-by-Step Solution:

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

2. **Dividing the Magnet**:
When the magnet is divided into two equal parts, the length of each part becomes half of the original length. Therefore, if the original length is \(L\), the length of each part after division will be:
\[ L' = \frac{L}{2} \]

3. **Pole Strength of Each Part**:
The pole strength of the magnet remains the same when it is divided along its length. Thus, the pole strength of each part remains:
\[ m' = m \]

4. **Calculating the Magnetic Moment of Each Part**:
Now, we can calculate the magnetic moment of each part using the formula for magnetic moment:
\[ M' = m' \times L' \]
Substituting the values we have:
\[ M' = m \times \frac{L}{2} \]
Since we know that \(M = m \times L\), we can express the magnetic moment of each part as:
\[ M' = \frac{M}{2} \]

5. **Conclusion**:
Therefore, the magnetic moment of each part after dividing the magnet into two equal parts is:
\[ M' = \frac{M}{2} \]

### Final Answer:
The magnetic moment of each part will be \(\frac{M}{2}\).

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