Question

Obtain the formula for the torque acting on a rectangular coil carrying current, suspended in a uniform magnetic field.

Answer 1

Let PQRS be the rectangular coil,

Force (F1) acting on the side PQ,

F1 = I(PQvector * Bvector)

F1 = I PQ.B sin theta = I l B sin90

Hence, F1 = IlB

Force (F2) acting on QR,

F2 = I(QRvector * Bvector) = I PQ. B sin theta = I b B sin theta

Force (F3) acting on RS

F3 = I(RS vector * Bvector) = I RS.B sin theta = IlB sin90 = IlB

Force (F4) acting on SP,  

F4 = I(SPvector * Bvector) = I SP>B sin theta = IbB sin theta

Torque = force * arm of couple = BIl * bcos theta = BIlbcos theta = BIA cos theta

Torque for the coil = torque * Number of turns = BINA cos theta