question_answer

A thin bar magnet of length\[2L\]is bent at the mid-point so that the angle between them is\[{{60}^{o}}C\]. The new length of the magnet is

A) \[\sqrt{2}L\]                                      

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

C) \[2\,\,L\]                             

D)        \[L\]

Correct Answer: D

Solution :

On bending the magnet, the length of the magnet                 \[AC=AB+BC\]                        \[=L\sin \left( \frac{\theta }{2} \right)+L\sin \left( \frac{\theta }{2} \right)\]                       \[=2L\sin \left( \frac{\theta }{2} \right)=2L\,\,\sin \,\,{{30}^{o}}\]                       \[=2L\times \frac{1}{2}=L\]