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

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.

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.