What is Faraday's law of induction?

Wrap wire into a coil, join its ends to a meter, and push a magnet in. The needle kicks. Hold the magnet still and the needle falls back to zero, even with the magnet deep inside. Pull it out and the needle kicks the other way. Michael Faraday found this on 29 August 1831.

The magnet's field lines loop from its north pole round to its south. The amount of field passing through the coil is the magnetic flux, Φ, measured in webers (Wb). For a flat coil in an even field it is Φ = B × A × cos θ: field strength times area, times how squarely the coil faces the field.

Faraday's law: the voltage made in a coil equals how fast the flux through it changes, times the number of turns. ℰ = −N × dΦ/dt. Move faster and the same change happens in less time, so the voltage is bigger. Twice the turns, twice the voltage.

The minus sign is Lenz's law. The current always flows so that the coil's own magnetism fights the change. Push a north pole in and the coil's near end becomes a north pole that pushes back. Pull it away and that end turns south and tugs it back. That's why you must do work to make electricity: it isn't free.

Spin a coil in a steady field instead and its flux rises and falls smoothly, so it makes a sine wave of alternating voltage. That is a generator, and it is how almost all the world's electricity is made.

Faraday's very first discovery was two coils wound on one iron ring. Switch a current on in one and a needle kicks on the other, though no wire joins them. A current makes flux; changing flux makes a voltage. That is mutual induction.

A transformer feeds the first coil, the primary, with AC. Its flux swings back and forth fifty times a second round an iron core, and passes through the secondary. Every turn of wire on the core feels the same volts, so the voltages go as the turns: V₂ ÷ V₁ = N₂ ÷ N₁. A phone-charger style transformer with 1,150 turns on the 230 V side and 60 on the other gives 12 V.

A home inverter (UPS) uses one backwards: its electronics chop the 12 V battery into AC and a 1 : 19 transformer lifts it to 230 V. A microwave oven steps 230 V up to about 2,000 V for its magnetron. See UPSClear and MicrowaveClear.

Why AC? Feed a transformer steady DC and the flux stops changing, so the secondary gets nothing. Worse, only the thin wire's resistance limits the primary's current, and it cooks. That's a big reason the world's grids run on AC.

A wireless phone charger is a transformer with the core taken out and a gap in the middle. Its flat coil runs at over 100,000 cycles a second. Lift the phone or slide it off-centre and less flux reaches the phone's coil, so charging slows and more power turns to heat.

An electric motor and a generator are the same machine. Push current in and it turns; turn it and current comes out. Induction is at work either way.

A desk or ceiling fan uses an induction motor. The coils round the outside, the stator, are fed AC in a pattern that makes a rotating magnetic field. In the middle sits a squirrel cage: aluminium or copper bars joined by rings, with no wires going in at all.

The rotating field sweeps past the bars, the flux through each loop of the cage changes, and Faraday's law drives current round the cage. Lenz's law says that current fights the change, so the cage gets dragged along after the field. It can never quite catch up: at the same speed the flux would stop changing and the push would vanish. The gap is the slip. See FanClear.

Other home machines use cousins of this. A mixer's universal motor has brushes and a wound rotor, and a modern washing machine uses a brushless DC motor driven by electronics. Spin any of them by hand and they make a voltage, the back-EMF, which rises with speed and holds the current down. See MixerClear and WasherClear.

An electric car uses this on purpose. Lift off the accelerator and the motor becomes a generator: the wheels spin it, it makes current that charges the battery, and Lenz's drag slows the car. That is regenerative braking. See CarClear.

An electric guitar has no microphone. Under the strings sits a pickup: small magnets wrapped in a coil of thousands of turns of hair-thin wire. The magnets magnetise the steel strings just above them.

Pluck a string and it swings towards and away from the magnet hundreds of times a second. Each swing changes the flux through the coil a little, and Faraday's law turns that into a tiny voltage that copies the string's motion. The amplifier makes it loud. The voltage follows the string's speed, so a higher note of the same size gives more signal. Fit a nylon string and there is no signal at all. See GuitarClear.

An induction hob runs a flat coil at tens of thousands of cycles a second. The changing flux induces swirling eddy currents in the pan's base, and their I²R heating cooks the food. The glass top only warms up from the hot pan.

The pan matters. In magnetic iron and steel the currents crowd into a skin only about 0.2 mm thick, and iron resists current far more than aluminium, so they heat strongly. Aluminium conducts too well and isn't magnetic, so a basic hob barely heats it and usually refuses to start. Glass has no free electrons at all.

Induction gets about 85% of its energy into the pan. A gas flame loses much of its heat round the sides. See ChimneyClear.

Drop a strong magnet down a copper pipe and it drifts down like a feather, though copper isn't magnetic. As the magnet falls, the flux through each ring of the pipe changes, so eddy currents swirl round the pipe above and below it. By Lenz's law they oppose the fall: the ring below pushes up, the ring above pulls up. The faster it falls, the harder they push, so it settles at a slow terminal speed. A plastic pipe has no free electrons, and the magnet just drops. Trains, roller coasters and gym bikes use this silent eddy-current braking.

Myth-buster: “A transformer that steps 12 V up to 230 V makes extra energy.” No! Voltage goes up, but current goes down by the same factor. Power in = power out, minus a few percent of heat in the copper and iron. Induction moves energy around. It never makes it.

Superconductors push this to the limit. With zero resistance, induced currents never die away, so a superconductor keeps the flux through it frozen. Lower one onto a magnet and it floats, locked in place: quantum levitation.

The biggest surprise came from James Clerk Maxwell in the 1860s. He wrote Faraday's law together with the other rules of electricity and found that a changing magnetic field makes an electric field, and a changing electric field makes a magnetic one. Each can keep the other going as a wave, travelling at c = 1 ÷ √(μ₀ε₀), the speed of light. Light, radio, Wi-Fi and X-rays are all induction chasing itself through space.