Question

A rectangular coil of wire carrying a current is suspended in a uniform magnetic field. The plane of the coil is making an angle of ${30}^{\circ }$ with the direction of the field and the torque experienced by it is ${\tau }_1$ and when the plane of the coil is making an angle of ${60}^{\circ }$ with the direction of the field the torque experienced by it is ${\tau }_2$, then the ratio ${\tau }_1$ : ${\tau }_2$ is :

• A. $1:\sqrt{3}$
• B. $\sqrt{3}:1$
• C. $1:3$
• D. $3:1$

Answer 1

Answer: (B)

$\sqrt{3}:1$

${\tau }_1=\overrightarrow{M}\times \overrightarrow{B}=MB\sin {60}^o$
${\tau }_2=\overrightarrow{M}\times \overrightarrow{B}=MB\sin {30}^o$
If coil is making an angle of $\theta$ with field, then it makes an angle of $(90-\theta )$ with area vector, i.e. magnetic moment vector.
$\therefore \frac{{\tau }_1}{{\tau }_2}=\frac{\sqrt{3}}{1}$