Torque on a Current Loop

A loop of current carrying wire placed in a uniform magnetic field (B) experiences no net force but a torque acts on it. This torque tends to rotate the loop to bring its plane perpendicular to the field direction. This is the principle that underlines the operation of all electric motors, meters, etc.

The sides ad and bc of the loop are parallel to B. So no force will act on them. Sides ab and cd are however, perpendicular to B, and these experience maximum force.

F_ab = F_cd and these act in opposite directions. Therefore, there is no net force on the loop. Since F_ab and F_cd do not act along the same line, they exert a torque on the loop that tends to turn it. This holds good for a current loop of any shape in a magnetic field.

In case the plane of the loop were perpendicular to the magnetic field, there would neither be a net force nor a net torque on it.

Torque = force ×perpendicular distance between the force

τ = B IL. b sin θ

θ is the angle between the magnetic field Band the normal to the plane of the coil.

τ = NBIL bsin θ

where N is the number of turns of the coil.

τ = NBI A sin θ

where A is area of the coil = L x b

|τ|= |B| |M| sin θ

where M = NIA is known as the magnetic moment of the current carrying coil.

Thus, the torque depends on B, A, I, N and θ.

If a uniform rotation of the loop is desired in a magnetic field, you need to have a constant torque. The couple would be approximately constant if the plane of the coil were always along or parallel to the magnetic field. This is achieved by making the pole pieces of the magnet curved and placing a soft iron core at the centre so as to give a radial field. The soft iron core placed inside the loop would also make the magnetic field stronger and uniform resulting in greater torque.