A magnetised wire of magnetic moment `'M'` and length `'l'` is bent in the form of a semicircle of radius `'r'`. The new magnetic moment is

Options

A. `(M)/(pi)`
B. `(2Mr)/(l)`
C. `(M)/(2pi)`
D. `(M)/(4pi)`

Explanation

To find the new magnetic moment of a magnetized wire that has been bent into the shape of a semicircle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment \( M \) of a bar magnet is given by the product of its pole strength \( m \) and its length \( l \):
\[ M = m \cdot l \]

2. **Finding Pole Strength**:
From the equation above, we can express the pole strength \( m \) as:
\[ m = \frac{M}{l} \]

3. **Bending the Wire**:
When the wire is bent into a semicircle of radius \( r \), the length of the wire remains the same, which is \( l \). The distance between the north and south poles of the semicircle configuration is now the diameter of the semicircle, which is:
\[ \text{Distance} = 2r \]

4. **New Magnetic Moment Calculation**:
The new magnetic moment \( M' \) of the semicircular wire can be calculated using the new distance between the poles and the pole strength:
\[ M' = m \cdot (2r) \]
Substituting the value of \( m \) from step 2:
\[ M' = \left(\frac{M}{l}\right) \cdot (2r) \]

5. **Final Expression for New Magnetic Moment**:
Thus, we can express the new magnetic moment \( M' \) as:
\[ M' = \frac{M \cdot 2r}{l} \]

### Conclusion:
The new magnetic moment of the wire bent in the form of a semicircle is:
\[ M' = \frac{2Mr}{l} \]