The DC Motor & Its Cousins

The brushed DC motor of this module still ships by the billion — toys, toothbrushes, car seat adjusters, anywhere cheap and simple wins. Its noblest descendant hides the commutator in software: the brushless DC motor in drones, electric vehicles and laptop fans keeps the coil stationary, spins the magnets, and lets transistors switch the coil currents at exactly the right rotor angles — the split-ring's half-turn reversal performed electronically, with nothing to wear out. The rotor position is often read by Hall-effect sensors (that story is The Hall Effect), closing a neat loop within this chapter. The cousins thrive too: every phone holds several voice-coil actuators — speaker, haptic buzzer, the camera's autofocus lens — and mechanical relays still click inside cars and appliances wherever a cheap milliamp must safely command tens of amps.

The skeleton motor of every board diagram has six labelled parts, and the labels themselves earn marks. A rectangular coil sits between the N and S poles of a permanent magnet, free to spin on an axle. The coil's ends are soldered to the two halves of a split-ring commutator — a copper cylinder sawn in two, each half insulated from the other, rotating with the coil. Two stationary brushes (graphite blocks in real machines) press lightly against the commutator and connect it to the battery.

Trace the current with a finger: battery → brush → half-ring → into side AB (current toward you in the diagram) → around the far end → back along side CD (current away from you) → the other half-ring and brush → battery. The two long sides carry the same current in opposite directions across the same field — that asymmetry is the engine.

Each long side of the coil is a straight current-carrying conductor in a field, so each feels the force Force on a Current-Carrying Conductor established: magnitude $F = BIL$, direction by Fleming's left-hand rule — First finger Field, seCond finger Current, thuMb Motion. For side AB (current toward you) the force comes out upward; for CD (current away from you), downward. Equal forces, opposite directions, separated by the coil's width — a couple, and the coil turns about its axle. The short sides carry current parallel or antiparallel to the field, and a current along the field feels no force at all. Only the two long sides push — a detail IGCSE examiners test directly.

Follow the coil through half a revolution and a crisis appears. Starting with its plane parallel to the field, the couple is at full strength and the coil accelerates. As it turns, the lever arms shrink; at a quarter turn — plane perpendicular to the field — the turning moment is exactly zero. This is the dead centre. Worse: if momentum carries the coil past it, the same forces now turn it backwards. An unmodified coil on a battery does not rotate; it swings to dead centre, overshoots, gets pushed back, and shudders to a halt like a compass needle finding north. The fix must reverse the current through the coil at exactly the moment it crosses dead centre — then the "backwards" push becomes a forwards push, every half-turn, forever. The split-ring commutator does it with sliding contacts: the ring's two insulated halves rotate with the coil, so each brush touches whichever half-ring is on its side at that moment. Every half-turn the halves swap brushes — and with them, the direction of current around the coil.

Note the choreography: at dead centre itself the brushes momentarily sit on the insulating gaps — no current, no torque — and the coil's momentum carries it across. On the far side the swapped connections drive the reversed current and the rotation continues. The coil's current reverses every half-turn while the battery never notices. That is the sentence to write when a paper asks the commutator's function: it reverses the current in the coil every half revolution, so that the torque on the coil always acts in the same rotational direction.

The one-coil skeleton lurches — full torque, fading, zero, full again. Real motors smooth and strengthen it with four standard upgrades, each worth a line in a "practical improvements" answer.

Many turns. Torque scales with $N$: two hundred turns give two hundred times the couple of one.

Several coils, angled apart. Wind three or more coils on the same axle at different angles, each with its own commutator segment pair; whichever coil is near its strongest position carries the drive, so the torque never falls near zero. This is why real commutators have many segments, not two.

A soft-iron armature core. The coils are wound on an iron cylinder. Iron funnels the field (the same job the core does in The Moving-Coil Galvanometer), making it effectively radial in the gap — torque near maximum through most of each rotation — and strengthening it manyfold.

Curved pole pieces and carbon brushes. Curved poles hug the armature to shape that radial field; graphite brushes lubricate their own sliding contact, spring-loaded to survive vibration and cheap to replace as they wear. One honest sentence belongs here, ahead of its full story. A spinning coil sweeps through the field — and a moving coil in a field generates a voltage (the dynamo effect, the motor effect's mirror image). This induced voltage opposes the driving battery and grows with speed: hence the big switch-on current that shrinks once the motor spins, and the overheating of a stalled motor — no motion, no back-voltage, maximum current. The full accounting belongs to the induction chapter; the qualitative sentence is all any board asks.

The loudspeaker is the motor effect with the axle removed and the current made to wiggle. A voice coil — a small cylinder of fine wire attached to the neck of a paper or polymer cone — sits in the circular gap of a permanent magnet shaped so the field is radial across the gap. An amplifier drives the audio signal through the coil as a current that swings positive and negative in the exact pattern of the sound wave. Each moment, the force on the coil is $F = BIL$ along the cylinder's axis: current one way, cone pushes out; current the other way, cone pulls in. The cone shoves the air back and forth, and the pressure ripples reach your ear as sound. Everything audible is encoded in that current: frequency of wiggle → pitch; size of wiggle → loudness. The numbers are more athletic than they look — the competitive worked example below puts a real cone at twenty times gravitational acceleration.

The relay swaps the force on a current for the pull of an electromagnet, and buys something neither the motor nor the speaker offers: isolation. A small control current — milliamps from a sensor or a dashboard switch — energises a coil on a soft-iron core; the electromagnet attracts a hinged iron armature, whose movement closes (or opens) contacts in a completely separate circuit carrying the heavy current of a starter motor or mains equipment. Cut the control current and a return spring pulls the armature back. A low-power, safe circuit throws a high-power, dangerous one, with no electrical connection between them — why the relay, born in the telegraph age, still clicks inside every car and washing machine you counted in the overview.

Board level — label, explain, and one calculation (ICSE pattern)

The diagram shows a simple DC motor with a 200-turn rectangular coil, sides 5.0 cm (in the field) by 4.0 cm, carrying 3.0 A between poles providing a field of 0.25 T. (a) Name the parts P (two half-rings) and Q (contacts pressing on P) and state the energy conversion. (b) State the function of P. (c) Calculate the force on each 5.0 cm side. (d) Find the turning moment when the coil's plane is parallel to the field.

Step 1. (a) P is the split-ring commutator; Q are the brushes. Energy conversion: electrical energy → kinetic (rotational mechanical) energy, with some loss as heat in the coil.

Step 2. (b) The scoring sentence: the commutator reverses the direction of current in the coil every half rotation, so that the torque acts in the same direction and the coil rotates continuously.

Step 3. (c) Each long side carries the coil current through all $N$ turns: $F = NBIL = 200 \times 0.25 \times 3.0 \times 0.050 = \boxed{7.5\ \mathrm{N}}$ per side — one side pushed up, the other down, by Fleming's left-hand rule.

Step 4. (d) The two forces form a couple across the 4.0 cm width: moment $= F \times w = 7.5 \times 0.040 = \boxed{0.30\ \mathrm{N\,m}}$. (Check via the area form: $NBIA = 200 \times 0.25 \times 3.0 \times 2.0\times10^{-3} = 0.30\ \mathrm{N\,m}$ — same answer, as it must be.)

Competitive level — the loudspeaker as a numbers machine (IGCSE-extended/ISC pattern, the hardest tier these boards ask)

A loudspeaker's voice coil has 40 turns of mean circumference 6.0 cm and sits in a radial field of 1.0 T. The amplifier drives a peak current of 0.50 A. The coil-and-cone assembly has mass 6.0 g. Find (a) the effective length of wire in the field, (b) the peak force on the coil, (c) the peak acceleration of the cone, and (d) explain what property of the current sets the pitch of the sound.

Step 1. (a) Every turn sits fully in the radial gap, so all its length counts: $L = NC = 40 \times 0.060 = \boxed{2.4\ \mathrm{m}}$ of wire — folded into a cylinder barely 2 cm across.

Step 2. (b) The radial field is perpendicular to the wire everywhere around the circle, so the full force law applies with no angle factor (the galvanometer gap's trick): $F = BIL = 1.0 \times 0.50 \times 2.4 = \boxed{1.2\ \mathrm{N}}$ along the axis — every part of the circular coil pushes the same way.

Step 3. (c) Newton's second law on 6.0 g: $a = F/m = 1.2 / 0.0060 = \boxed{200\ \mathrm{m/s^2}}$ — about 20 times $g$. This is why cones are engineered light and stiff: they are flung back and forth at these accelerations thousands of times per second.

Step 4. (d) The force direction tracks the current direction instant by instant, so the cone vibrates at the frequency of the alternating audio current — that frequency is the pitch. (Loudness rides on the current's amplitude, through the force.) Timing note: 4–5 minutes as a structured question. Parts (a)–(c) are one-line calculations; the separating marks are the radial-field justification in (b) and the frequency sentence in (d) — write both explicitly.

Naming imprecision. "Commutator" alone can drop the mark — ICSE mark schemes want split-ring commutator, and "brushes" for the stationary contacts. Label arrows on diagrams: field N→S, current from the + terminal, force by Fleming's left hand.

The function sentence, mangled. Weak: "the commutator keeps the motor spinning." Scoring: reverses current + every half turn + torque same direction — three ideas, three chances to lose.

Forces on the wrong sides. Only the sides perpendicular to the field feel a useful force; the sides parallel to it feel none. Naming the force-carrying pair on the diagram is often a required point.

The double-reversal trick. Battery reversed AND poles swapped = no change. Count the flips (see the warning box).

Left hand for motors, right hand for generators. Fleming's left-hand rule covers this whole module; the right-hand (dynamo) rule belongs to induction. Crossing hands under pressure is the most literal mark-loser in physics — physically put your left hand on the desk.

Which boards ask what. This module is ICSE Class 10 and IGCSE core/extended territory (descriptive + $F = BIL$-level calculation). CBSE Class 12, JEE and NEET do not carry the DC motor — their Chapter 4 marks live in the galvanometer and conversion modules. ICSE's "working not required" means torque mathematics beyond the simple couple is not demanded, but parts, function sentences and Fleming's rule very much are. (Heads-up for later cohorts: CISCE's newly published 2028 syllabus drops the motor from ICSE — check your exam year's specification.)

Constants: none needed beyond the given data; there is no $g$, no $\mu_0$ in this module's questions.

Texts. ICSE Concise Physics X (Selina), Electromagnetism chapter — the board-canonical parts-and-functions treatment · Cambridge IGCSE Physics (Sang), Electromagnetic effects · NCERT Class 10 Science, Magnetic Effects of Electric Current (the CBSE Class-10 cousin).

Provenance. All numbers recomputed: $F = 200\times0.25\times3.0\times0.050 = 7.5\ \mathrm{N}$; moment $= 7.5\times0.040 = 0.30\ \mathrm{N\,m} = NBIA$ with $A = 2.0\times10^{-3}\ \mathrm{m^2}$; speaker $L = 40\times0.060 = 2.4\ \mathrm{m}$, $F = 1.0\times0.50\times2.4 = 1.2\ \mathrm{N}$, $a = 1.2/0.0060 = 200\ \mathrm{m/s^2}$.

Prerequisites. Force on a Current-Carrying Conductor (F = BIL and Fleming's left-hand rule) · Current Loops as Magnetic Dipoles: Torque & Moment (the couple, in full generality). Leads to. The AC Generator (the same machine run backwards, in the induction chapter) · The Hall Effect (the sensor that tells a brushless motor where its rotor is) · The Moving-Coil Galvanometer (the same couple, tamed by a spring).