Question

An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle 60° with each other. The magnetic moment of this new magnet is :

• A. M
• B. \(\frac{M}{2}\)
• C. 2M
• D. \(\frac{M}{\sqrt3}\)

Answer 1

The Correct Option is B

Step 1: Recall the Definition of Magnetic Moment

The magnetic moment is proportional to the product of pole strength and the effective length of the magnet:

$$ M = m \cdot L $$

Where:

\( M \) = Magnetic moment

\( m \) = Pole strength

\( L \) = Effective length of the magnet

Step 2: Analyze the New Configuration

When the bar is bent at an angle of 60°, the effective length is reduced to half of the original length:

$$ L_{\text{effective}} = \frac{L}{2} $$

Step 3: Calculate the New Magnetic Moment

The new magnetic moment is given by:

$$ M_{\text{new}} = m \cdot L_{\text{effective}} $$

Substituting the value of \( L_{\text{effective}} \):

$$ M_{\text{new}} = m \cdot \frac{L}{2} = \frac{M}{2} $$

Step 4: Conclusion

The new magnetic moment is \( \frac{M}{2} \).

When a bar magnet is bent, its effective length decreases, reducing the magnetic moment.