Torque on a coil

If a coil carrying a current is placed in a magnetic field it will experience a force on two of its sides in such a way as to make the coil rotate.

A rectangular coil with sides of length a and b is placed in a magnetic field of flux density B and free to rotate about an axis perpendicular to the paper. A current of I Amps flows in the coil. The field exerts a force (F) on the sides of the coil of length b of = BNIb

Torque on the coil = BANI sinq

where A = ab, the area of one face of the coil.
The maximum torque occurs when the plane of the coil is lying along the field lines (q = 90^o and sin q = 1).

Maximum torque (Co) = BANI