An iron bar of length has magnetic moment . It is bent at the middle of its length such that the two arms make an angle with each other. The magnetic moment of this new magnet is [2024]

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Solution

Q.
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 [2024]

1 $M$

2 $\frac{M}{2}$

3 $2$ $M$

4 $\frac{M}{\sqrt{3}}$

Ans.
(2)

$M_{net} = \sqrt{{(\frac{M}{2})}^{2} + {(\frac{M}{2})}^{2} + 2 \frac{M}{2} \cdot \frac{M}{2} \cos 120 °}$

$M_{net} = \sqrt{\frac{M^{2}}{4} \times 2 - \frac{M^{2}}{4}} = \sqrt{\frac{M^{2}}{4}} = \frac{M}{2}$

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