question_answer

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

A) \[\sqrt{2}\,L\]    

B) \[\sqrt{3}\,L\]

C) \[2\,L\]             

D) \[L\]

Correct Answer: D

Solution :

[d] When the magnet is bent, the length of the magnet is: \[AC=AB+BC\] \[=L\sin \frac{\theta }{2}+L\sin \frac{\theta }{2}\] \[=2L\sin (\theta /2)=2L\,sin(60{}^\circ /2)\] \[=2L\sin 30{}^\circ =L\]