question_answer

Two bar magnets with magnetic moments 2 M and M are fastened together at right angles to each other at their centres to form a crossed system, which can rotate freely about a vertical axis through the centre. The crossed system sets in earth?s magnetic field with magnet having magnetic moment 2M making and angle q with the magnetic meridian such that                                                                          [AFMC 1999]

A)            \[\theta ={{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]     

B)            \[\theta ={{\tan }^{-1}}\left( \sqrt{3} \right)\]

C)            \[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\]     

D)            \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\]

Correct Answer: C

Solution :

           \[\Rightarrow \tan \theta =\frac{M}{2M}=\frac{1}{2}\Rightarrow \theta ={{\tan }^{-1}}=\frac{1}{2}\]