Left: magnet & coil animation. Right: EMF vs time plot. Current arrows show Lenz's law direction.
Electromagnetic induction, discovered by Michael Faraday in 1831, is the production of an electromotive force (EMF) in a conductor exposed to a changing magnetic flux. Faraday's law states ε = −dΦB/dt: the induced EMF equals the rate of change of magnetic flux through the circuit, with the negative sign (Lenz's law) indicating that the induced current opposes the change. This principle underlies virtually every electrical generator, transformer, and induction motor on Earth.
This simulation animates a magnet moving through a coil, showing how the speed of motion and number of coil turns affect the magnitude of the induced EMF. You can also compare AC generator and transformer configurations to see how the same principle is applied in different engineering contexts.
What is Faraday's law of induction?
Faraday's law states that the induced EMF in any closed loop equals the negative rate of change of magnetic flux through it: ε = −dΦB/dt. For a coil with N turns, the EMF is multiplied: ε = −N dΦB/dt. If the flux changes at 1 Wb/s through a 100-turn coil, the induced EMF is 100 V. This single equation explains generators, transformers, and induction cookers.
What is Lenz's law?
Lenz's law states that the direction of the induced current is always such as to oppose the change in flux that caused it. If a magnet approaches a coil, the induced current creates a magnetic field repelling the magnet; if the magnet recedes, the induced field attracts it. This is a consequence of energy conservation: work must be done against the opposing force to maintain the motion.
How does moving a magnet faster affect the induced EMF?
Doubling the speed of the magnet doubles the rate of flux change (dΦB/dt), which doubles the induced EMF and the resulting current. The power delivered to the coil (P = ε²/R) therefore quadruples. This is why generators produce more power at higher rotational speeds, and why the mechanical torque required to turn them also increases with load current.
Each turn of the coil links the same changing flux, so each contributes −dΦB/dt to the total EMF. For N turns in series, ε = −N dΦB/dt. A 500-turn coil in the same field change produces 500 times the EMF of a single turn. This is the operating principle of transformers, where the turns ratio sets the voltage ratio.
Motional EMF arises when a conductor moves through a static magnetic field: free charges in the moving conductor experience a Lorentz force qv × B, driving a current. Transformer EMF arises when a stationary conductor sits in a changing magnetic field: the changing B directly induces an electric field via Faraday's law. Both are described by the same integral form of Faraday's law.
An AC generator (alternator) rotates a coil of N turns with area A at angular frequency ω in a uniform field B. The flux is Φ = NBA cos(ωt), so the induced EMF is ε = NBAω sin(ωt)—a sinusoidal voltage with peak value NBAω. A car alternator with N = 200 turns, A = 50 cm², B = 0.5 T, ω = 1000 rpm gives peak EMF ≈ 52 V.
When a motor spins, it also acts as a generator, producing a back-EMF that opposes the supply voltage. The net current is I = (V − εback)/R. At start-up the back-EMF is zero, so current is very high (which is why motors need starting resistors or soft-start electronics). At full speed, back-EMF ≈ V and current drops to a small value needed only to overcome friction and load.
Wireless chargers use inductive coupling: an alternating current in the transmitter coil creates a time-varying magnetic field, which induces an EMF in the receiver coil inside the device. The Qi standard operates at 87–205 kHz. At close range (a few millimetres), efficiencies above 85% are achievable. Resonant coupling (WPT) can extend the range to tens of centimetres with similar efficiency.
Mutual inductance M quantifies how much EMF is induced in coil 2 per unit rate of current change in coil 1: ε2 = −M dI1/dt. The unit is the henry (H). For two coils with self-inductances L1 and L2 and coupling coefficient k, M = k√(L1L2). A perfectly coupled (k = 1) transformer with M = 1 H induces 1 V in the secondary for every 1 A/s change in primary current.
Michael Faraday made the key discovery in August 1831, demonstrating that a changing current in one coil induced a brief current in a nearby coil. He also showed that moving a magnet in and out of a coil generated a current. Joseph Henry discovered mutual induction independently in the US around the same time but published later. Faraday's law was later formalised mathematically by James Clerk Maxwell.