Electromagnets and Electric Motors: How They Work in 3D

A needle that twitched

In 1820 Hans Christian Ørsted, in Copenhagen, saw a compass needle near a wire turn when the current was switched on. According to the usual account it happened during a demonstration. He published in July 1820 that electricity and magnetism are linked. The scene draws rings of field around the wire, and the needle turns to follow them. For a long straight wire B = μ₀I / (2πr), with μ₀ = 4π × 10⁻⁷ T·m/A. At 10 A and 5 cm, B = 2 × 10⁻⁷ × 10 / 0.05 = 4 × 10⁻⁵ T, or 40 µT, about the size of Earth's field.

The coil

Wind the wire into a coil, a solenoid, and the rings add up to one strong field along its axis. Inside, B = μ₀·n·I, where n is the number of turns per metre and I the current. A coil of 500 turns on 0.10 m has n = 5000 per metre; at 2 A, B = 4π × 10⁻⁷ × 5000 × 2 ≈ 0.0126 T, or 12.6 mT, with only air inside. Slide in a soft iron core and the field grows by hundreds of times, because the iron's domains line up. William Sturgeon built an early practical electromagnet in the 1820s. Switch the current off and the field vanishes.

Force on a wire

Put a wire with current into a magnetic field and it is shoved sideways. The force is F = B·I·L, where B is the field in tesla, I the current in amperes and L the length of wire inside the field in metres. With B = 0.5 T, I = 4 A and L = 0.10 m, F = 0.5 × 4 × 0.10 = 0.2 N. In 1821 Michael Faraday used this push to make a wire circle around a magnet, the first continuous electromagnetic rotation, and the idea of the electric motor was born.

The motor in the picture

The cutaway motor has a rectangular loop between two magnets. Current runs up one side and down the other, so the two sides are pushed opposite ways and the loop turns. After half a turn the push would reverse and stall it, so a split ring called the commutator swaps the current's direction just then. Brushes touch the ring and the loop keeps spinning. A stronger magnet, more loops or more current give more turning force. Practical DC motors followed in the 1830s. The sandbox lets you change the current and the turns.

Speakers and cars

A loudspeaker is a motor that does not spin: a coil glued to a cone sits in a magnet's field. The music signal makes the current vary, the force F = B·I·L pushes the cone back and forth, and the cone moves the air. With 5 m of wire in a 1 T field carrying 1 A, the force is 1 × 1 × 5 = 5 N. An electric car uses a motor of the same family. At 25 m/s (90 km/h), a motor delivering 50 kW pushes the car with F = P / v = 50,000 / 25 = 2,000 N.

Trains that float

Maglev trains lift off the track. In one design electromagnets under the train pull up towards the rail; in another, superconducting magnets and coils in the guideway lift and push. With no wheels touching, the main drag is air. The Shanghai Maglev has carried passengers since 2004 at up to 431 km/h, which is 431 / 3.6 ≈ 120 m/s. A Japanese test train reached 603 km/h in 2015. In the scene the coils along the track switch on in turn, like a motor unrolled into a straight line.

Electromagnets and motors