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.

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. The right-hand slap or palm rule gives the same result.

Two parallel current-carrying wires illustrate the force directly: each wire sits in the magnetic field of the other, so each feels a force $F = BIL$. Currents in the same direction attract, currents in opposite directions repel. This mutual force is in fact how the ampere was historically defined, linking the unit of current to a measurable mechanical force between conductors.

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 current-on-a-wire force is just the sum of these forces on all the moving charges in the conductor.

Torque on a current loop

A rectangular coil of $N$ turns and area $A$ carrying current $I$ in a field $B$ experiences a torque:

where $\phi$ is the angle between the coil plane and the field. Torque is maximum when the coil plane is parallel to the field and zero when the coil plane is perpendicular to it. The two sides of the coil that lie across the field feel forces in opposite directions (because the current runs opposite ways in them), and this couple is what turns the coil. This is the principle of the moving-coil meter and the DC motor.

The DC motor

A direct current motor converts electrical energy into rotational kinetic energy using the motor effect. A current-carrying coil sits in a magnetic field, and the opposing forces on its two sides produce a torque. 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. Practical motors use several coils and a multi-segment commutator to smooth the turning and avoid dead spots.

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, and remember to include $\sin\theta$ whenever the wire is not perpendicular to the field.