A steel wire of length 'l' has a magnetic moment 'M'. It is bent in 'L' shape having equal size of arm. The new magnetic moment is

Answer

To find the new magnetic moment of a steel wire bent into an 'L' shape, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Condition**:
- The steel wire has a length \( l \) and a magnetic moment \( M \). The magnetic moment is defined as the product of the pole strength and the length of the wire.

2. **Bending the Wire**:
- When the wire is bent into an 'L' shape, each arm of the 'L' will have equal lengths. Since the total length of the wire is \( l \), each arm will have a length of \( \frac{l}{2} \).

3. **Magnetic Moment of Each Arm**:
- The magnetic moment for each arm can be calculated using the formula:
\[ M' = m \cdot \frac{l}{2} \]
- Here, \( m \) is the pole strength. Since the total magnetic moment \( M \) is given by \( M = m \cdot l \), we can express the magnetic moment for each arm as:
\[ M_1 = M_2 = \frac{M}{2} \]

4. **Direction of Magnetic Moments**:
- Assume the first arm (vertical) has a magnetic moment \( M_1 \) directed upwards, and the second arm (horizontal) has a magnetic moment \( M_2 \) directed to the right.

5. **Resultant Magnetic Moment**:
- The resultant magnetic moment \( M_R \) can be found using the Pythagorean theorem since the two arms are perpendicular to each other:
\[ M_R = \sqrt{M_1^2 + M_2^2} \]

6. **Substituting the Values**:
- Substitute \( M_1 \) and \( M_2 \):
\[ M_R = \sqrt{\left(\frac{M}{2}\right)^2 + \left(\frac{M}{2}\right)^2} \]
- This simplifies to:
\[ M_R = \sqrt{2 \cdot \left(\frac{M}{2}\right)^2} = \sqrt{2} \cdot \frac{M}{2} \]

7. **Final Expression**:
- Thus, the new magnetic moment \( M_R \) can be expressed as:
\[ M_R = \frac{M}{\sqrt{2}} \]

### Conclusion:
The new magnetic moment of the steel wire bent into an 'L' shape is:
\[ \text{New Magnetic Moment} = \frac{M}{\sqrt{2}} \]