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A thin bar magnet of length $2 L$ is bent at the mid-point so that the angle between them is $60^{\circ}$. The new length of the magnet is
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Verified Answer
The correct answer is:
$L$
On bending the magnet, the angle between two parts of the magnet is expressed in diagram below
Now, the minimum distance between the ends $P$ and $R$
$\begin{aligned} & =L \sin 30^{\circ}+L \sin 30^{\circ} \\ & =2 L \sin 30^{\circ}=2 L \sin 30^{\circ} \\ & =2 L \times \frac{1}{2}=L\end{aligned}$
Now, the minimum distance between the ends $P$ and $R$
$\begin{aligned} & =L \sin 30^{\circ}+L \sin 30^{\circ} \\ & =2 L \sin 30^{\circ}=2 L \sin 30^{\circ} \\ & =2 L \times \frac{1}{2}=L\end{aligned}$
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