Question

$M$ and $M\sqrt{3}$ are the magnetic dipole moments of the two magnets, which are joined to form a cross figure. The inclination of the system with the field, if their combination is suspended freely in a uniform external magnetic field $B$ is

• A. $\theta ={30}^{\circ }$
• B. $\theta ={45}^{\circ }$
• C. $\theta ={60}^{\circ }$
• D. $\theta ={15}^{\circ }$

Answer 1

The correct option is C $\theta ={60}^{\circ }$

$Given:$ $M$ and $M\sqrt{3}$ are the two magnetic dipole moments of two magnets.

$Solution:$ Let the magnet having magnetic moment $M$ makes an angle $\theta$ with the magnetic field. Then, the magnet having magnetic moment $\sqrt{3}M$ makes an angle $(90-\theta )$ with the magnetic field. In equilibrium, both the torques are balanced. MB $\sin \theta =\sqrt{3}MB\sin (90-\theta )=$

$\sqrt{3}MB\cos \theta$

$\Rightarrow \tan \theta =\sqrt{3}=\tan {60}^{\circ }$

$\theta =60^{\circ }$

$So,the$ $correct$ $option:C$