Question

A circular coil of 30 turns and radius 8·0 cm carrying a current of 6 A is suspended vertically in a uniform horizontal magnetic field of 1·0 T. The field lines make an angle of 30\(^{\circ}\) with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged?

Hint:

Always read carefully whether the given angle is with respect to the normal to the plane (\(\theta\)) or with the plane of the coil itself (\(\alpha\)). If it is with the plane, use \(\tau = N I A B \cos\alpha\) or translate it via \(\theta = 90^{\circ} - \alpha\). Also, torque is shape-independent as long as the boundary lies in a single flat plane and encloses the same area.

Answer 1