DIY · Card 42 · Engineering · Electromagnetism
A coil of bare copper wire, a battery and six magnets. Push the battery into the coil and it shoots off on its own, carrying its own electromagnet with it, so it never has to stop.
01The brief
Build a train that drives itself through a coil of wire, with no motor and no wheels.
3
parts: a coil of bare copper, a battery and the magnets on its ends
4 A
or so of current through the coil: nearly a short circuit, which is why it is so lively
1879
the year the first electric passenger train carried people round a fairground in Berlin
Most toys that move have a motor, gears and wheels. This one has none. It is a battery with a magnet on each end, and it zooms through a coil of copper wire as if pulled on a string.
The trick is that the train builds its own track as it goes. Only the short stretch of coil between the two magnets carries current, so only that stretch becomes an electromagnet, and it always pushes the train onwards. It uses the same magnet-and-current push as the homopolar motor and the coil of the nail electromagnet.
02Kit
A reel of bare copper, a battery and a stack of strong magnets.
Tick off what you have
0 of 5 ready
03Method
Wind and stretch a coil, put the magnets on the battery the right way round, and push it in.
Step 1 of 8 · Minute 0
You need a reel of bare (uncoated) copper wire about 1 mm thick, an AAA battery, six neodymium disc magnets a little wider than the battery, a wooden dowel a little wider than the magnets, and tape.
The train doesn’t move at all.
Why
The magnets face the same way along the battery, so the forces cancel.
Fix
Turn one stack of magnets over, so the same pole faces outwards at both ends.
It moves a little, then stops.
Why
Turns of the coil are touching, or the battery is flat.
Fix
Stretch the coil so every turn is separate, and try a fresh battery.
It jams in the coil.
Why
The magnets are too wide for the coil, or the coil is squashed.
Fix
Wind a new coil on a slightly wider dowel, and keep it round.
04Physics
Neodymium magnets are coated in nickel, which conducts electricity. When the train is in the coil, the magnets touch the bare copper, and a circuit is complete: out of the battery, through one magnet, round and round the coil to the other magnet, and back into the battery. Current only flows in the short stretch of coil between the magnets.
Current flowing round a coil turns it into an electromagnet, with a field running along its middle. The magnets at the two ends sit right where that field begins and ends, and each feels a push or a pull. Build the train and see what makes it go:
Current
4.3 A
Speed
60 cm/s
Battery flat in
7 min
Like poles face outwards, so the coil pushes one magnet and pulls the other in the same direction. Turn the battery round, or both magnets, and it drives the other way.
Why must the poles face out the same way? Freeze the train and look at the two forces. A magnet at the end of an electromagnet is pulled in or pushed out depending on which way it faces. Point the magnets opposite ways and the two forces line up; point them the same way and they cancel exactly:
With the same pole facing out at both ends, one magnet is pushed out of the coil and the other is pulled in, and both forces point the same way. The train moves, taking its electromagnet with it, so it never catches up.
The models use a typical AAA battery and the simple rule that a magnet on an electromagnet’s axis feels a force proportional to how fast the field changes along it. Real trains wobble and rub; the directions are the real ones.
05The big idea
Bring the push
with you.
A magnet pulled towards a coil stops when it gets there. This train never gets there, because the coil that pulls it moves along with it. The electromagnet is wherever the train is, always just ahead and just behind.
Every electric motor solves the same problem. Something has to keep switching the push so that the moving part is always chasing a field it never catches. In a motor it is a commutator or a chip; in your train, it is simply where the magnets touch the wire.
06The math
1 · The current
I = V ⁄ (r + R)
A battery of voltage V and internal resistance r drives current through a coil of resistance R.
2 · The coil’s field
B = μ₀ n I
Inside a coil with n turns per metre carrying current I.
3 · The push on a magnet
F = m dB ⁄ dx
A magnet of moment m feels a force where the field changes along its axis, strongest at the coil’s ends.
The coil between the magnets is only a few centimetres of copper, with a resistance of about 0.05 Ω. A fresh AAA battery has an internal resistance of roughly 0.3 Ω, so I = 1.5 ⁄ 0.35 ≈ 4 A. With about 6 turns per centimetre, n = 600 per metre, and the field inside is B = 1.26 × 10⁻⁶ × 600 × 4 ≈ 3 mT, about sixty times Earth’s.
That field rises from nothing to its full value over roughly the width of the coil, a centimetre, right where the magnets sit. A strong neodymium stack with m ≈ 0.5 A·m² then feels about F ≈ 0.5 × 0.003 ⁄ 0.01 ≈ 0.15 N, and the two ends together twice that: plenty to shove a 25-gram train along. And a battery giving 4 A is flat in about seven minutes.
07Real life
Roller coasters, catapults and the fastest train in the world all use your train’s trick at full scale.
Roller coaster launches
Many modern roller coasters don’t climb a lift hill. Rows of electromagnets along the track switch on in sequence and fling the train forward, from standstill to motorway speeds in a couple of seconds. It is your coil, unrolled and switched by computer.
Aircraft carrier catapults
The newest American aircraft carriers launch planes with an electromagnetic catapult instead of steam. A long linear motor in the deck accelerates a shuttle, and the jet hooked to it, to take-off speed in about a hundred metres.
Maglev records
In 2015 a Japanese superconducting maglev train reached 603 km/h on a test line, the fastest any train has gone. Magnets lift it clear of the guideway and coils along the track pull it forward, with nothing touching at all.
Linear-motor metros
Some underground lines, including the Toei Ōedo Line in Tokyo, are driven by linear motors: a coil under each train pushes against a metal strip between the rails. The trains can be smaller and climb steeper slopes than wheel-driven ones.
Hard drives
The arm that swings the read head across a spinning hard disk is moved by a voice coil: a coil of wire between strong magnets. Current one way swings it in, the other way swings it out, thousands of times a second and to within a fraction of a micrometre.
Electric motors everywhere
An ordinary motor is your train bent into a circle: coils and magnets arranged so the push never stops. The simplest one, a battery, a magnet and a wire, has its own card.
1879
At the Berlin trade exhibition of 1879, Werner von Siemens’s company laid a small oval of track and ran a tiny electric locomotive round it, pulling open carriages. Current reached it through a third rail between the running rails. Over the summer it carried tens of thousands of passengers at about walking pace.
It was the first electric railway to carry passengers. Within two years Siemens had built an electric tram line in Lichterfelde near Berlin, and within decades electric trains were running under and between the world’s cities. Your coil-and-battery train is that idea stripped to its bare bones.
08Is and isn’t
The magnets are attracted to the copper.
Copper isn’t magnetic. A magnet won’t stick to the coil at all. The force comes only from the current flowing in the coil, which turns it into an electromagnet for as long as the current flows.
It’s a perpetual motion machine.
It runs on the battery, and fast. Several amps flow, and a little AAA battery is flat within minutes. When it dies, the train stops.
Any wire will do.
The wire must be bare copper. Most craft wire is coated with plastic or a clear enamel, which stops the magnets making contact, and no current flows.
The more magnets, the faster.
Up to a point. Stronger magnets feel a bigger push, but they also add weight and friction against the coil. Three on each end is a good balance.
09Go further
A
Speed trap
Time the train over 30 cm of coil and work out its speed. Then try a battery that has been used. How much slower is it?
B
Uphill
Prop one end of the coil on a book. How steep a slope can the train climb before it stalls?
C
Magnet count
Try one, two, three and four magnets on each end. Which gives the fastest train?
D
Figure of eight
Can you bend a long coil into a loop, or a figure of eight, that the train will run round without jamming?
E
Compass check
Hold a compass beside the coil as the train passes. Watch the needle twitch as the moving electromagnet goes by.
10Questions
Wind bare copper wire into a tight coil round a dowel a little wider than your magnets, then stretch it so the turns don’t touch. Put three neodymium disc magnets on each end of an AAA battery, with the same pole facing out at both ends. Push the battery into the coil and it drives itself through.
The magnets conduct electricity and touch the bare coil, so current flows from the battery through the stretch of coil between them. That stretch becomes a short electromagnet. It pushes the magnet at one end and pulls the magnet at the other, both in the same direction, so the train moves, carrying its electromagnet with it.
Usually because the magnets face the wrong way. They must have the same pole facing outwards at both ends; if they point the same way along the battery, the two forces cancel. Also check that the wire is bare, not enamelled, and that the coil’s turns aren’t touching each other.
The direction depends on the current and the way the magnets face. Put the train in the coil the other way round, or flip both magnet stacks, and it drives the other way.
Only a few minutes of running. The coil and magnets have almost no resistance, so the battery is nearly short-circuited and several amps flow. The battery and the coil get warm, so take the train out between runs.
Safety · Use only an ordinary AAA battery, never a lithium or rechargeable pack, and take the train out between runs: the battery and coil get hot. Neodymium magnets pinch and shatter, and must be kept from small children.
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