Torque on a Current-Carrying Rectangular Coil
This 3D simulation isolates the forces acting on each side of a rectangular current-carrying coil placed in a uniform magnetic field, and shows how they combine into a turning effect. Rotating the coil while watching the force arrows explains where the cosine in the torque formula comes from.
How to use this simulation
- Rotate the coil to any orientation in the field
- Change the current, field strength and number of turns
- Toggle the force vectors on and off
What to look for
- Torque is maximum when the coil plane is parallel to the field
- Torque falls to zero when the coil plane is perpendicular to the field, even though the forces are still there
- Forces on the sides parallel to the field cancel and never contribute
The physics behind it
The two sides perpendicular to the field carry current in opposite directions and feel forces F = BIL in opposite directions, forming a couple. The torque is τ = BIAN·cosθ, where θ is the angle between the coil plane and the field. The other two sides produce forces that act along the same line and simply cancel, contributing no torque.