§-Syllabus dot point

WAPhysicsSyllabus dot point

How does a magnetic field exert a force on a current-carrying conductor?

Apply the motor effect to forces on current-carrying conductors and the operation of DC motors

A focused answer to the WACE Year 12 Physics Unit 3 content point on the motor effect. The force on a current-carrying wire, the right-hand rule for direction, the torque on a current loop, and how a DC motor produces continuous rotation.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

WACE wants you to calculate the force on a current-carrying conductor, find its direction, and explain how this motor effect drives a DC motor. This builds on the force on a single moving charge and scales it up to a whole current.

Force on a straight conductor

A length $L$ of wire carrying current $I$ in a field $B$ feels a force

F=BIL\sin\theta,

where $\theta$ is the angle between the current direction and the field. The force is greatest when the wire is perpendicular to the field ( $\theta=90^\circ$ ) and zero when it lies along the field ( $\theta=0$ ). The force is always perpendicular to both the current and the field.

Finding the direction

Use the right-hand rule: point the fingers in the direction of the conventional current, curl toward the field, and the thumb (or palm push) gives the force. An equivalent statement points the fingers along the current and the palm along the field so the thumb shows the force. State the result as a clear direction such as "into the page" or "upward".

Torque on a current loop

In a rectangular loop in a field, the two sides carrying current perpendicular to the field feel equal and opposite forces. These do not cancel as a turning effect because they act on opposite sides of the axis, so they produce a torque that rotates the loop. The torque is maximum when the loop plane is parallel to the field and zero when the plane is perpendicular (the forces then act along the same line).

How a DC motor keeps turning

A DC motor is a current loop in a magnetic field free to rotate. As the loop turns, the torque would reverse once the loop passes the plane perpendicular to the field, which would stall it. A split-ring commutator solves this by reversing the current direction in the loop every half turn, so the torque always pushes the same way and the loop spins continuously. Brushes maintain electrical contact with the rotating commutator.

Parallel wires and the definition of the ampere

Two long parallel wires carrying currents each sit in the magnetic field created by the other, so each feels a force given by the motor effect. If the currents flow the same way the wires attract; if they flow in opposite directions they repel. This mutual force per unit length is the basis of the historical definition of the ampere. In an exam you may be asked to predict whether two wires attract or repel: find the field one wire makes at the other (using the right-hand grip rule), then apply $F=BIL$ with the right-hand rule to the second wire. The symmetry means each wire pushes or pulls the other equally, a Newton's third law pair.

Scaling up to a coil

A single wire experiences $F=BIL\sin\theta$ , but a coil of $N$ turns multiplies the effect, since each turn feels the force, so the total turning effect on a loop scales with $N$ . This is why real motors use many-turn coils and why the torque on a coil is often written as proportional to $NBIA$ , where $A$ is the loop area. Increasing the number of turns, the current, the field strength or the coil area all raise the torque, which gives four practical design levers for a more powerful motor. The same four factors appear (as a rate of change) when the device is run in reverse as a generator, which is why the motor and generator are so closely linked.

Stating direction and angle

Always identify $\theta$ as the angle between the current and the field, not between the wire and the plates or anything else. When asked for direction, name your hand rule and give an unambiguous final direction. For a motor, mention the commutator explicitly when explaining continuous rotation, as that is the marked point.

Exam-style practice questions

Practice questions written in the style of SCSA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WACE 20226 marksA horizontal wire of length

0.30\ \text{m}

and mass

1.5\ \text{g}

lies perpendicular to a uniform horizontal magnetic field of

0.40\ \text{T}

. (a) Calculate the current needed so that the magnetic force on the wire balances its weight. (b) State the direction the current must flow relative to the field for the force to be upward.

Show worked answer →

A 6 mark calculation rewards equating forces, solving for current and a direction.

(a) Required current. For the magnetic force to support the wire, $BIL=mg$ , so

I=\frac{mg}{BL}=\frac{(1.5\times10^{-3})(9.8)}{(0.40)(0.30)}=\frac{1.47\times10^{-2}}{0.12}=0.12\ \text{A}.

(b) Direction. Using the right-hand rule, the current must flow horizontally and perpendicular to the field such that $F=BIL$ points vertically upward; reversing the current would push the wire down. A correct statement names the perpendicular orientation that gives an upward force.

Markers reward $BIL=mg$ , the weight $mg=1.47\times10^{-2}\ \text{N}$ , $I=0.12\ \text{A}$ and a valid right-hand-rule direction.

WACE 20215 marksExplain how a split-ring commutator allows a simple DC motor to rotate continuously in one direction, and explain what would happen to the rotation if the commutator were replaced by slip rings.

Show worked answer →

A 5 mark explanation needs the torque-reversal problem, the commutator fix and the slip-ring consequence.

The stalling problem: A current loop in a field experiences a torque that turns it, but once the loop passes the plane perpendicular to the field, the forces on its sides would reverse the torque and tend to push it back, so it would oscillate rather than spin.
The commutator fix: A split-ring commutator reverses the current direction in the loop every half turn, at the moment the loop passes through the perpendicular plane. This keeps the torque acting in the same rotational sense, so the loop continues turning the same way.
With slip rings instead: Slip rings keep the current direction in the loop fixed, so the torque would reverse each half turn and the loop would simply oscillate back and forth about the perpendicular position rather than rotating fully.

Markers reward the torque-reversal issue, the half-turn current reversal by the commutator, and the oscillation result for slip rings.