The Motor Effect

Put a current-carrying wire across the gap of a horseshoe magnet, switch the current on, and the wire is pushed sideways out of the gap (or pulled in, depending on the direction of the current). This sideways push is the motor effect.

Why does it happen? The current creates its own magnetic field (4.7.2.1, right-hand grip rule) — concentric circles around the wire. This field combines with the steady field of the magnet. On one side of the wire the two fields add together (stronger field); on the other side they partially cancel (weaker field). The wire is pushed from the strong-field side toward the weak-field side.

When is the force a maximum? When the wire is at right angles (90°) to the magnetic field. At smaller angles only the component of B perpendicular to the wire contributes to the force.

When is the force zero? When the wire is parallel to the field. The wire's own circular field then lies in the same plane as the magnet's field and there is no asymmetry to push it sideways.

A practical demonstration ('jumping wire' experiment). A length of bare wire is loosely supported between two horseshoe-magnet pole faces. When the switch closes, current flows; the wire jumps sideways or rolls along the rails depending on the geometry. Reverse the battery polarity, and the wire jumps the other way. Use a stronger magnet or a higher current, and the wire jumps harder. This simple demo is the seed of every electric motor.

Foundation vs Higher. Foundation Tier candidates learn that the wire experiences a force; Higher Tier candidates use Fleming's left-hand rule and calculate the force with $F = BIL$.

Fleming's left-hand rule lets you predict the direction of the force on a current-carrying conductor in a magnetic field — without doing any maths.

How to apply the rule.

1. Hold your left hand with the thumb, first finger and second finger all at right angles to each other (like an L-shape with thumb pointing up).
2. Point the First finger in the direction of the magnetic Field (N → S).
3. Point the seCond finger in the direction of the conventional Current (+ → − in the external circuit).
4. Your thuMb then shows the direction of the Motion (force) on the conductor.

The memory aid: FBI in alphabetical order — Force, B-field, Current. Or the FFC memory: First Finger Field, seCond finger Current, thuMb Motion.

Important — use your left hand, not your right. The right-hand rule is for the grip rule (direction of field around a wire). Different rules for different jobs.

Conventional current vs electron flow. AQA uses conventional current — positive flow direction — for Fleming's rule. If a question gives you electron flow (negative to positive), reverse the direction before applying the rule.

Fleming's LEFT-hand rule F-B-I: First finger = Field, seCond finger = Current, thuMb = Motion.

A worked check. A horizontal wire carries current westward, in Earth's magnetic field that points northward. Which way does the wire feel a force?

• First finger: north (field).
• Second finger: west (current).
• Thumb: downward (force).

The wire is pushed downward. Now reverse the current to eastward → thumb points upward; the wire is pushed up. Reverse both current and field → thumb again points downward (cancellations).

Tricks to avoid mistakes in the exam.

1. Use your left hand only. Sit on your right hand if you have to.
2. Conventional current — flip electron-flow questions before applying the rule.
3. Mutually perpendicular — your three fingers must be at 90° to each other; if you can't make the geometry work, the situation isn't perpendicular and the force is less than maximum (or zero if parallel).

For a current-carrying conductor at right angles to the field, the size of the force on the wire is:

$F = B \, I \, L$

• $F$ — force on the conductor (newtons, N).
• $B$ — magnetic flux density of the field (tesla, T).
• $I$ — current in the conductor (amperes, A).
• $L$ — length of conductor in the magnetic field (metres, m).

What is flux density? It's a measure of how strong a magnetic field is at a point. Unit: tesla (T). 1 T is a very strong field — the field between the poles of a strong neodymium fridge magnet is about 0.1–0.5 T. The Earth's field is only about $5\times10^{-5}$ T (= 50 µT).

Worked example 1. A 0.20 m length of wire lies at right angles to a magnetic field of flux density 0.30 T. A current of 4.0 A flows through the wire. Calculate the force on the wire.

$F = BIL = 0.30 \times 4.0 \times 0.20 = 0.24\,\text{N}$

Worked example 2 — finding I. A wire of length 0.50 m carries an unknown current at 90° to a magnetic field of flux density 0.40 T. The force on the wire is 1.0 N. Find the current.

$I = \dfrac{F}{BL} = \dfrac{1.0}{0.40 \times 0.50} = 5.0\,\text{A}$

Important constraint — perpendicular only. $F = BIL$ as written assumes the wire is at 90° to B. If the angle is smaller, the force is less. (The general form is $F = BIL\sin\theta$ — not required at GCSE.) If a question describes the wire as 'parallel' to the field, the force is zero.

Equation sheet. $F = BIL$ is on the AQA Physics equation sheet (2024+), but you should still know it cold for speed.

To make the force on a current-carrying conductor stronger:

1. Increase the current (I) — more amperes, more force.
2. Increase the magnetic flux density (B) — use a stronger magnet (e.g. neodymium instead of ceramic), or pack more magnets together.
3. Increase the length (L) of conductor in the field — a longer wire or many turns of a coil all share the same field.
4. Ensure the wire is at 90° to the field — any tilt reduces the effective length perpendicular to B.

To reverse the direction of the force:

• Reverse the current (swap the battery terminals). The wire jumps the opposite way.
• OR reverse the field (swap the magnet so N and S are swapped). Same effect.
• BUT reversing both at the same time cancels out — the force returns to its original direction. (This is exactly why an AC motor without a commutator does not spin in one direction — the alternating current would push the coil one way then back the other; a commutator solves this by reversing the connection to the coil every half-turn, see 4.7.2.3.)

Why this matters for electric motors. A motor is just a coil of wire in a magnetic field. By controlling I and B you control how hard the motor pushes. By reversing the current with a commutator (or DC controller) you make the coil spin instead of just oscillating. Modern UK railway traction motors, electric-car drives, hair dryers, food blenders — all rely on this physics.

Force on a moving charge. A single moving charged particle in a magnetic field also feels a force; this is the same physics that bends the path of charged particles in a CRT (cathode-ray tube) or particle accelerator. Not on the AQA spec but a useful link.

Imagine a single rectangular loop of wire sitting between the poles of a horseshoe magnet, with the magnetic field running horizontally from N to S across the gap.

When a current flows through the loop:

• On one side of the loop, the conventional current flows (say) toward you.
• On the opposite side, the same current flows the other way — away from you.

Both sides sit in the same magnetic field (N → S), but carry current in opposite directions. Applying Fleming's left-hand rule:

• One side experiences a force upward.
• The opposite side experiences a force downward.

The two equal-and-opposite forces form a couple — a pair of forces that creates a turning effect (a moment) rather than moving the whole loop in one direction. The loop rotates about its central axis.

What about the top and bottom of the coil? The ends of the rectangular loop carry current parallel to the magnetic field, so by spec 4.7.2.2 they feel zero force. Only the two long sides perpendicular to the field contribute to the turning effect.

What about a coil with many turns? Each turn adds another pair of opposite forces, so a coil of N turns produces N times the turning effect of a single loop. That's why real motors use multi-turn coils on a soft iron core.

Simple DC motor Split-ring commutator reverses I every half-turn → coil keeps spinning.

brush brush split-ring

Without a commutator, a DC current would push one side of the coil up and the other side down — until the coil reached the vertical position. At that point, the forces would still act, but they would now stop the coil rotating further (they would pull it back). The coil would simply oscillate and stop.

A split-ring commutator fixes this. It is a metal ring split into two halves (separated by tiny insulating gaps), attached to the ends of the coil and to the rotating shaft. Two stationary carbon brushes (held against the commutator by springs) deliver the current from the battery to whichever half of the ring they happen to be touching.

How it keeps the motor turning.

1. At any instant, brush A touches one half-ring, brush B touches the other. Current flows through the coil in one direction. One side of the coil is pushed up, the other down → the coil rotates by 90°.
2. As the coil approaches the vertical position, the gap in the commutator passes the brushes — momentarily breaking the circuit.
3. As the coil rotates past vertical, brush A now touches the other half-ring (and brush B touches the first half-ring). The current through the coil has reversed.
4. With the current reversed, the side of the coil that's now on the left is pushed up (it used to be the right side, pushed up; geometry is the same). The coil continues to rotate in the same direction.

In short: the split-ring commutator reverses the direction of the current in the coil every half-turn, so the force on each side of the coil keeps pushing it the same way round.

Brushes — usually carbon — slide against the commutator and conduct current while allowing rotation. They wear down over time (which is why cheap motors die: the brushes wear out, not the magnets).

AC vs DC. A DC motor uses a split-ring commutator. An AC motor doesn't need one — the current naturally reverses 50 times a second (UK mains), and the motor is designed so the field reverses in step. (AC motors are not on AQA spec 4.7.2.3 — DC only.)

To predict which way a DC motor will spin, apply Fleming's left-hand rule to one side of the coil. Because the opposite side carries current in the opposite direction, the rule will give a force in the opposite direction on that side too — and those two forces together rotate the coil.

Worked example. A horizontal coil sits between a left-hand N pole and a right-hand S pole. The conventional current on the near side flows toward you; on the far side it flows away from you.

• Near side: First finger → right (N to S), second finger → out of the page (toward you), thumb → down. Force is downward on the near side.
• Far side: First finger → right (N to S), second finger → into the page (away from you), thumb → up. Force is upward on the far side.

Together: near side pushed down, far side pushed up → the coil rotates so the far side comes up and the near side goes down.

How to reverse the direction of rotation.

1. Reverse the current — swap the battery terminals (or reverse the polarity of a DC controller). Both forces flip.
2. Reverse the magnetic field — swap the magnets so N is on the right and S is on the left. Both forces flip.
3. Do NOT reverse both — that returns the motor to its original direction.

These rules underpin the direction switch on a cordless drill, the reverse gear in an electric car, and the up/down control on a window-blind motor.

The size of the turning effect on the coil depends on the same factors as the simple motor-effect force (4.7.2.2). To make a DC motor spin faster or push harder:

1. Bigger current (I). Connect a higher voltage supply or reduce the resistance of the coil. More amperes → bigger force on each wire.
2. Stronger magnetic flux density (B). Use stronger permanent magnets (e.g. neodymium instead of ceramic) or use an electromagnet with a soft iron core for the field.
3. More turns on the coil (N). Each turn that lies in the field contributes another pair of forces. N turns → N × the turning effect.
4. A soft iron core (armature). Wrapping the coil around a soft iron block concentrates the magnetic field through the coil, increasing the effective B. Soft iron magnetises and demagnetises easily — perfect for a part that needs to flip its magnetism quickly.

Limits. Real motors are limited by:

• Resistance heating: high current overheats the coil, damaging the insulation.
• Brush wear: high currents and high speeds wear the brushes faster.
• Back EMF (not on GCSE): a spinning coil generates its own EMF that opposes the supply.

Energy transfers in a motor. Electrical energy from the supply → kinetic energy of the rotating coil + heat (from resistance and friction) + sound. A typical small DC motor is around 50–80 % efficient; large industrial motors can exceed 95 %.

A standard moving-coil loudspeaker has three essential parts:

1. Permanent magnet. A strong cylindrical magnet (often neodymium or ferrite) with a circular gap. The magnetic field in the gap is radial — it points outward from the central pole to the outer ring (or vice versa).
2. Voice coil. A small cylindrical coil of fine copper wire wound on a paper or aluminium former. The coil sits inside the gap of the magnet, free to slide in and out (along the axis of the cone).
3. Paper cone (diaphragm). A flexible paper or plastic cone glued at its narrow end to the voice coil. The wide end is attached to a flexible suspension (the 'surround') that lets the cone move in and out but keeps it centred.

When an alternating current flows in the voice coil, the motor effect produces a force on each turn of the coil. Because the field in the magnet's gap is radial and the current circles around the coil, the force pushes the coil along its axis — into or out of the magnet gap. The coil drags the cone with it, and the cone pushes air molecules to make sound.

sound waves

Alternating current → coil oscillates in radial field → cone vibrates → sound waves.

Apply an alternating current (AC) to the voice coil. At any instant the current flows in one direction around the coil — and by Fleming's left-hand rule, the force on the coil pushes it (say) outward from the magnet, taking the cone with it.

Half a cycle later, the AC reverses. The current now flows the other way round the coil → Fleming's left-hand rule gives a force in the opposite direction → the coil is pulled inward, dragging the cone with it.

So:

• Current flowing one way → cone pushed outward.
• Current reversed → cone pulled inward.
• Repeat at the AC frequency → cone vibrates back and forth.

The vibrating cone pushes against air molecules. When the cone moves outward it compresses the air (creating a compression); when it moves inward it leaves a region of lower-pressure air (a rarefaction). A train of compressions and rarefactions travels away from the speaker — this is a longitudinal sound wave (linking to spec 4.6.1.1).

Frequency of the sound = frequency of the AC. If the music signal contains a 440 Hz note (concert pitch A), the AC through the coil oscillates at 440 Hz, the cone vibrates at 440 Hz, and the sound wave has a frequency of 440 Hz.

Loudness depends on current amplitude. A bigger current → a bigger F = BIL force → larger cone displacement → larger pressure swings in the air → louder sound. Cranking up your volume knob increases the amplitude of the AC supplied to the coil.

Real music is a complex AC signal. It contains many frequencies and amplitudes at once. The coil and cone respond to all of them, reproducing the original sound. This is why a loudspeaker is a transducer — it converts a signal from one form (electrical) to another (mechanical/acoustic).

Headphones and earbuds work on exactly the same principle as loudspeakers, just at a smaller scale. Each earpiece contains:

• A tiny permanent magnet with a small radial gap.
• A miniature voice coil inside the gap.
• A thin plastic or Mylar diaphragm glued to the coil — equivalent to the loudspeaker cone but much smaller and lighter.

When AC flows through the coil, the diaphragm vibrates and pushes air directly into the ear canal. Because the diaphragm is so small and light, it can respond to very high frequencies (up to 20 000 Hz) with excellent accuracy.

Why use headphones instead of speakers? Headphones place the sound source millimetres from your eardrum, so they need only a tiny fraction of the power. A typical headphone draws around 1 mW per channel; a small bookshelf loudspeaker draws several watts.

Stereo. Two separate channels (left and right) carry slightly different AC signals to the two earpieces. Each cone/diaphragm reproduces its own signal, creating the illusion of sound coming from different positions.

In-ear vs over-ear. The physics is identical; in-ear models (earbuds) sit just outside the ear canal, while over-ear (full-size) headphones surround the whole pinna. AQA does not require you to know specific styles.

Worked example — comparing magnitudes. A loudspeaker driving an 8 Ω voice coil with 1.0 A at 100 Hz has $F = BIL = 0.8 \times 1.0 \times 0.05 = 0.04 \text{ N}$ acting on each side of the coil (assuming B = 0.8 T and the wire length in the field is 50 mm). The cone — much heavier than air — moves only a fraction of a millimetre, but that's enough to drive the air for many metres in a room.

Two qualities of a sound — its pitch and its loudness — are controlled by two different features of the AC signal driving the voice coil.

Pitch (frequency). Determined by the frequency of the alternating current. High-frequency AC → cone vibrates fast → high-frequency sound → high-pitched note. The human ear can detect sound from about 20 Hz to 20 000 Hz (see spec 4.6.1.3 sound waves). A treble note like a violin's top E sits around 660 Hz; a deep bass-guitar note around 40 Hz.

Loudness (amplitude). Determined by the amplitude of the alternating current (the size of the current swings). Larger I → larger F = BIL → cone moves further from its rest position → bigger pressure swings in the air → louder sound. A volume knob on an amplifier scales the AC amplitude going to the coil.

Why doesn't increasing B make the speaker louder? It would — but B is fixed by the permanent magnet and can't be changed by the user. Manufacturers do use stronger magnets in 'high-sensitivity' speakers and in studio monitors.

Distortion. If the AC amplitude is too big, the coil moves so far it bangs against the end of the magnet gap, or the cone bends instead of moving smoothly. The output sound no longer matches the input signal — this is distortion. AQA doesn't ask about distortion directly but it's a good real-world link.

The complete chain.

$\text{Music source}\ \longrightarrow\ \text{AC signal}\ \longrightarrow\ \text{Voice coil}\ \longrightarrow\ \text{Force (F = BIL)}\ \longrightarrow\ \text{Cone vibration}\ \longrightarrow\ \text{Sound wave}$