Physics • Year 12 • Module 6 • Lesson 9
Torque on a Current-Carrying Coil
Lock in the torque formula, the angle convention, and the roles of the radial field and split-ring commutator before tackling calculations.
1. Term–definition match
The definitions below are shuffled. Write the matching term from this list in the right-hand column: torque, number of turns (n), angle θ, radial magnetic field, split-ring commutator, couple, coil plane, uniform magnetic field, maximum torque, zero torque. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A turning force on an object; the product of force and perpendicular distance from the pivot. Measured in N m. | |
| 1.2 | The angle between the plane of the coil and the direction of the external magnetic field. Used in τ = nBAI cos θ. | |
| 1.3 | A field whose lines always point toward or away from a central axis, keeping the field perpendicular to the coil sides at all rotational positions. | |
| 1.4 | A device in a DC motor that reverses the current direction every half-turn, ensuring the torque always acts in the same rotational direction. | |
| 1.5 | The number of individual loops wound in a coil; doubling this doubles the torque for the same B, A, and I. | |
| 1.6 | A pair of equal and opposite parallel forces whose lines of action do not coincide, producing a net turning effect with no net linear force. | |
| 1.7 | The flat surface enclosed by one loop of the coil; its orientation relative to B determines the lever arm for each side force. | |
| 1.8 | A field with the same magnitude and direction at every point in space; produces a torque that varies as cos θ as the coil rotates. | |
| 1.9 | The torque on a coil when its plane is parallel to the magnetic field (θ = 0°); equal to nBAI. | |
| 1.10 | The torque on a coil when its plane is perpendicular to the magnetic field (θ = 90°); the coil is at the equilibrium position. |
2. True or false — with correction
Circle T or F for each statement. If false, write the corrected version on the line below. 12 marks (1 T/F + 1 correction each)
2.1 Torque on a current-carrying coil is maximum when the coil plane is perpendicular to the magnetic field. T / F
2.2 The angle θ in τ = nBAI cos θ is measured between the plane of the coil and the magnetic field direction. T / F
2.3 Doubling the number of turns in a coil doubles the torque, because each turn contributes its own force couple. T / F
2.4 In a radial magnetic field, the torque on a rotating coil varies with cos θ, producing a pulsing output. T / F
2.5 Without a split-ring commutator, the coil of a DC motor would oscillate back and forth rather than rotate continuously. T / F
2.6 The maximum torque on a coil is achieved when the normal to the coil plane is parallel to the magnetic field. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
couple · cos θ · half-turn · maximum · nBAI · parallel · radial · zero
A rectangular coil carrying current in a magnetic field experiences a force on each of its two sides perpendicular to the field. These equal and opposite forces form a ___________ that produces a torque. The torque is given by τ = ___________ × ___________, where the second factor accounts for the coil’s orientation relative to the field. Torque is ___________ when the plane of the coil is ___________ to the field (θ = 0°), and drops to ___________ when the plane is perpendicular. In a DC motor, a ___________ magnetic field is used so that the field is always perpendicular to the coil sides, keeping the torque nearly constant. The split-ring commutator reverses the current every ___________, ensuring the torque always acts in the same rotational direction.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State the formula for torque on a current-carrying coil and identify every variable. Which variable is most commonly confused in HSC exams?
4.2 Explain why, in a uniform magnetic field, the torque on a spinning coil varies between a maximum and zero during each half-rotation.
4.3 State the function of a radial magnetic field in a DC motor, and describe how curved pole pieces produce this type of field.
4.4 Explain what happens to the rotation of a DC motor coil if the split-ring commutator is replaced with a continuous (slip-ring) connection.
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “is maximised by”, “requires”, “depends on”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: torque · current (I) · coil area (A) · angle θ · radial field · split-ring commutator.
6. Annotate the torque formula
The formula τ = nBAI cos θ is shown in the box below. In each labelled space A–E, write the name and SI unit of the corresponding variable. The first one (A) is done for you. 8 marks (2 each for B–E)
| Symbol | Name of quantity | SI unit (name and abbreviation) |
|---|---|---|
| τ | Torque (given) | Newton metre (N m) (given) |
| n | ||
| B | ||
| A | ||
| I | ||
| θ |
Q1 — Term–definition match
1.1 torque • 1.2 angle θ • 1.3 radial magnetic field • 1.4 split-ring commutator • 1.5 number of turns (n) • 1.6 couple • 1.7 coil plane • 1.8 uniform magnetic field • 1.9 maximum torque • 1.10 zero torque.
Q2 — True / false with correction
2.1 False. Torque is maximum when the coil plane is parallel to the field (θ = 0°, cos 0° = 1). When perpendicular, the torque is zero.
2.2 True. θ is measured between the plane of the coil and B — not between the normal to the plane and B. This is a common HSC error.
2.3 True. Each extra turn adds an identical force couple; the effects add, so τ = nBAI.
2.4 False. In a radial magnetic field, the torque remains nearly constant (approximately equal to nBAI) throughout the rotation, because the field is always perpendicular to the coil sides. It is in a uniform field that torque varies as cos θ.
2.5 True. Without the commutator, when the coil passes the equilibrium (zero-torque) position, the torque would reverse, pushing it back — causing oscillation rather than continuous rotation.
2.6 False. Maximum torque occurs when the coil plane is parallel to B (θ = 0°). When the normal is parallel to B, the plane is perpendicular to B (θ = 90°), giving zero torque.
Q3 — Cloze paragraph
In order: couple / nBAI / cos θ / maximum / parallel / zero / radial / half-turn.
Q4.1 — Torque formula
τ = nBAI cos θ, where τ = torque (N m), n = number of turns (dimensionless), B = magnetic field strength (T), A = coil area (m²), I = current (A), θ = angle between coil plane and B (degrees or radians). The most commonly confused variable is θ — students often use the angle between the normal and B rather than the angle between the coil plane and B, which swaps sin and cos.
Q4.2 — Torque variation in a uniform field
In a uniform field, the perpendicular distance from the axis of rotation to the line of action of each side force (the lever arm) is proportional to cos θ. When the coil plane is parallel to B (θ = 0°), the lever arm is at maximum so torque is maximum (= nBAI). When perpendicular (θ = 90°), the forces act through the axis so the lever arm is zero and torque is zero.
Q4.3 — Radial field and curved pole pieces
A radial field ensures the magnetic field lines are always perpendicular to the sides of the coil at every rotational position (except at the vertical gap). This keeps cos θ ≈ 1 throughout rotation, delivering smooth, nearly constant torque rather than the pulsing torque of a uniform field. Curved (concave) pole pieces shaped around a cylindrical iron core concentrate and redirect field lines radially outward from the centre.
Q4.4 — Slip-ring instead of commutator
With a continuous slip-ring connection, the current direction in the coil never reverses. When the coil passes the zero-torque position, the torque would reverse direction, pushing the coil back toward the equilibrium point. The coil would oscillate back and forth around the equilibrium rather than completing full rotations.
Q5 — Sample concept map
Valid arrows include:
- torque — is proportional to → current (I)
- torque — is proportional to → coil area (A)
- angle θ — scales torque via → cos θ factor in τ
- radial field — holds θ constant, maximising → torque
- split-ring commutator — reverses current every half-turn to maintain direction of → torque
- split-ring commutator — works with → radial field for continuous rotation
Award 1 mark per valid labelled arrow (minimum 6 required; maximum 6 marked).
Q6 — Annotate the formula
n: number of turns (dimensionless / no unit). B: magnetic field strength, tesla (T). A: area of coil, square metres (m²). I: current, amperes (A). θ: angle between coil plane and B-field, degrees (°) or radians (rad) — dimensionless in calculation.
Award 1 mark for each correct name and 1 mark for each correct unit (4 marks for names + 4 marks for units = 8 marks for rows B–E, minus τ which is given).