Magnetism · Physics

Torque on a Current-Carrying Coil Simulation

A rectangular coil in a uniform field in 3D, with the force on every side drawn. The long sides form a couple of arm w cos θ, so τ = NBIA cos θ; the short sides' forces cancel along one line. Let it turn and it swings to face the field.

Interactive virtual lab · no download · works on phones and laptops

Chapter: Moving Charges and Magnetism
For: Class 12 · JEE · NEET
Time: ~12 min

Torque on a Current-Carrying Coil is a Pro simulation

Pro opens all 125 virtual labs — 483 simulations with guides and quizzes.

How to use it

1Rotate the coil with the angle slider.
2Change current, turns and field.
3Press play to let it turn freely.

What to notice

Torque is largest with the coil's plane along the field.
Zero torque when the plane faces the field — the forces are still there.
The forces on the sides parallel to B's plane cancel.

For teachers

A ready-made teaching kit comes with this lab

Lesson plan
19 min, 4 steps
Ask the class
3 questions with answers
Quick quiz
5 questions, printable
Key formulas
3 formulas

Unlock with Pro

About the Torque on a Current-Carrying Coil simulation

A rectangular coil carrying a current in a magnetic field feels forces on each side. This 3D simulation draws every one of them. The two sides perpendicular to the field feel F = NBIl in opposite directions, forming a couple; its arm is w cos θ, where θ is the angle between the coil's plane and the field. So the torque is τ = NBIA cos θ — largest with the plane along the field and zero when the coil faces the field.

The other two sides feel equal and opposite forces along the same line, so they cancel completely. Press play and the coil turns freely (with some friction) until it faces the field: there the forces are still present but they pull straight outward and have no turning effect. This is the principle behind electric motors and moving-coil meters.

Also covers: torque on a coil, nbia cos theta, current loop in magnetic field, magnetic moment, couple, motor principle.

Frequently asked questions

When is the torque on a current loop maximum?

When the plane of the coil is parallel to the field (its normal perpendicular to B). It is zero when the plane is perpendicular to the field.

Do the forces vanish when the torque is zero?

No. The forces on the sides are still there, but they act along a line through the axle, so they only stretch the coil.

Why does a motor need a commutator?

Without it the torque reverses after the coil passes the zero-torque position, so the coil would just rock. Reversing the current every half turn keeps the torque in one direction.