Describe the magnetic force on currents and charges and explain the operation of a DC motor.

What this dot point is asking

This dot point is about the motor effect: the force that a magnetic field exerts on moving charge, whether that charge flows as a current in a wire or moves as a free particle.

Force on a current-carrying conductor

When a straight conductor of length $L$ carrying current $I$ sits in a uniform magnetic field of strength $B$, it experiences a force:

where $\theta$ is the angle between the current direction and the field. The force is maximum when the wire is perpendicular to the field ($\theta = 90^\circ$) and zero when it is parallel to the field. The magnetic field strength $B$ is measured in tesla (T).

The direction of the force is perpendicular to both the current and the field. Use the right-hand rule: point your fingers in the direction of conventional current, curl them toward the field $B$, and your thumb gives the force. Many texts use the right-hand slap or palm rule with the same result.

Force on a moving charge

A single charge $q$ moving at speed $v$ through a field $B$ feels:

If the charge moves perpendicular to a uniform field, this force is constant in magnitude and always perpendicular to the velocity, so the charge follows a circular path, exactly like centripetal motion. Setting $qvB = \dfrac{mv^2}{r}$ gives the radius $r = \dfrac{mv}{qB}$.

The DC motor

A direct current motor converts electrical energy into rotational kinetic energy using the motor effect. A rectangular coil carrying current sits in a magnetic field. The two sides of the coil that lie across the field experience forces in opposite directions (because the current flows in opposite directions in them), producing a turning effect, or torque, on the coil.

The torque on a coil of $N$ turns and area $A$ is:

where $\phi$ is the angle between the coil plane and the field. Torque is maximum when the coil is parallel to the field and zero when the coil is perpendicular to it.

The key engineering problem is that as the coil passes through the vertical position the torque would reverse and stop the rotation. A split-ring commutator solves this by reversing the current direction in the coil every half turn, so the torque always acts to keep the coil rotating the same way.

When answering motor questions in the exam, describe the forces on each side of the coil, explain how they create a torque, and clearly state the role of the commutator in maintaining continuous rotation. A labelled diagram strongly supports your explanation.