Magnetic force on conductors: WACE Year 12 Physics Unit 3

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

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.