Question

A current-carrying coil experiences a torque due to a magnetic field. The value of the torque is 80% of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is

• A. \( 30^\circ \)
• B. \( 45^\circ \)
• C. \( \tan^{-1} \left(\frac{3}{4}\right) \)
• D. \( \tan^{-1} \left(\frac{4}{3}\right) \)

Hint:

Maximum torque occurs when the coil is perpendicular to the field (\(\theta = 90^\circ\)). At any other angle, use \(\sin\theta\) to find torque.

Answer 1

The Correct Option is D

The torque on a coil in a magnetic field is given by: \[ \tau = \tau_{\max} \sin\theta \] Given that \( \tau = 0.8 \tau_{\max} \), we solve for \( \theta \): \[ \sin\theta = 0.8 \] \[ \theta = \sin^{-1}(0.8) \] Using trigonometric identities, \[ \tan\theta = \frac{4}{3} \] Thus, the correct answer is \( \tan^{-1} \left(\frac{4}{3}\right) \).