NSW · HSCModule 6
DC motor torque calculator
τ = NBIA cos θ for a current-carrying rectangular coil in a uniform magnetic field. Set θ = 0 for maximum torque.
Inputs
Result
Torque τ
0.3000N·m
Maximum torque (θ = 0)
0.3000N·m
τ = NBIA cos θ. The split-ring commutator in a DC motor reverses the current as the coil passes the perpendicular position, keeping the torque in one direction.
How this calculator works
The calculator multiplies the number of turns, magnetic field, current, area, and cos θ. The result is the instantaneous torque on the coil; the split-ring commutator in a real motor flips the current to keep the torque positive throughout the rotation.
Common questions
- What is the torque formula for a coil?
- τ = NBIA cos θ, where N is the number of turns, B is the magnetic field, I is the current, A is the area of the coil, and θ is the angle between the coil plane and B. Maximum torque is at θ = 0.
- Why does the formula use cos θ, not sin θ?
- It depends on how θ is defined. If θ is between the coil plane and B, use cos. If θ is between the coil normal and B, use sin. This calculator uses the plane convention from the NESA syllabus.
- What does the split-ring commutator do?
- It reverses the current in the coil twice per revolution, ensuring that the torque always acts in the same rotational direction. Without it, the coil would oscillate rather than rotate.
- Why are the brushes called brushes?
- Originally they were literal brushes made of wire bristles to maintain electrical contact with the rotating commutator. Modern ones are graphite blocks but the name stuck.