A magnet of magnetic moment M of length 22 cm is bent into a semicircle.Now the magnetic moment is

Options

A. 11/7 M
B. 7/11M
C. 14M
D. 22M

Explanation

To solve the problem of finding the new magnetic moment \( M' \) when a magnet of magnetic moment \( M \) and length 22 cm is bent into a semicircle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The original length of the magnet is \( L = 22 \) cm.
- The magnetic moment is given as \( M \).

2. **Determine the Shape of the Magnet:**
- The magnet is bent into the shape of a semicircle.

3. **Calculate the Radius of the Semicircle:**
- The length of the semicircular arc is equal to the original length of the magnet.
- The length of a semicircular arc is given by \( \text{Length} = \pi r \).
- Setting this equal to the original length:
\[ \pi r = 22 \text{ cm} \]
- Solving for \( r \):
\[ r = \frac{22}{\pi} \]
- If we take \( \pi \approx \frac{22}{7} \):
\[ r = \frac{22 \times 7}{22} = 7 \text{ cm} \]

4. **Determine the Magnetic Length of the Semicircle:**
- The magnetic length \( L_m \) for a semicircle is twice the radius:
\[ L_m = 2r = 2 \times 7 \text{ cm} = 14 \text{ cm} \]

5. **Calculate the New Magnetic Moment \( M' \):**
- The magnetic moment is given by the formula:
\[ M' = m \times L_m \]
- Since the pole strength \( m \) remains the same, we can express the new magnetic moment as:
\[ M' = m \times 14 \text{ cm} \]

6. **Express the Original Magnetic Moment:**
- The original magnetic moment can be expressed as:
\[ M = m \times 22 \text{ cm} \]

7. **Find the Ratio of New Magnetic Moment to Original Magnetic Moment:**
- To find the ratio \( \frac{M'}{M} \):
\[ \frac{M'}{M} = \frac{m \times 14}{m \times 22} = \frac{14}{22} = \frac{7}{11} \]

8. **Final Expression for New Magnetic Moment:**
- Therefore, the new magnetic moment \( M' \) can be expressed as:
\[ M' = \frac{7}{11} M \]

### Conclusion:
The new magnetic moment when the magnet is bent into a semicircle is:
\[ M' = \frac{7}{11} M \]