Question

A current carrying coil is placed in an uniform magnetic field, with its plane parallel to the magnetic field. If the coil turns through angle $\theta$, the torque $\tau$ and $\theta$ are related as :

• A. $\tau\propto\sin\theta$
• B. $\tau\propto\cos\theta$
• C. $\tau\propto\tan\theta$
• D. $\tau\propto\cot\theta$

Answer 1

Answer: (B)

$\tau\propto\cos\theta$

Answer 2

For current carrying coil $\overrightarrow{p_m}$ is directed perpendicular to the plane of the coil. When the coil turns through angle $\overrightarrow{\theta}$, angle between $\overrightarrow{p_m}$ and $\overrightarrow{B}$ is (90 - $\theta$). Also $\overrightarrow{\tau} = \overrightarrow{p_m} \times \overrightarrow{B}$.