How Electromagnetic Induction Works: Faraday's Law

Electromagnetic induction is the reason electricity can be generated in power stations, stored in wireless chargers, and stepped up or down in the grid. Michael Faraday showed in 1831 that a changing magnetic field can push charges around a closed loop of wire. James Clerk Maxwell later wrapped that observation into his equations, and it remains one of the central results of classical electromagnetism.

This post explains magnetic flux, states Faraday's law and Lenz's law, works through a numerical example, and shows how the same principle appears in generators, transformers and induction cooktops.

Magnetic flux

Magnetic flux, written Φ, measures how much magnetic field passes through a surface. For a flat loop of area A in a uniform field B, Φ = B A cos θ, where θ is the angle between the field and the normal to the loop. The unit is the weber (Wb), equal to one tesla times one square metre.

Flux is maximal when the field passes straight through the loop and zero when the field runs parallel to its plane. Induction happens when flux through a loop changes. That change can come from a moving magnet, a changing current in a nearby coil, rotating the loop, or changing the loop area.

Faraday's law

Faraday's law says that the induced electromotive force (EMF) around a closed loop equals the negative rate of change of magnetic flux through it:

EMF = − dΦ / dt

For a coil of N turns, the total EMF is multiplied by N, because each turn contributes. The EMF is measured in volts. It is a potential difference, not a force, but it drives current in any closed circuit connected to the loop.

The rule does not care what causes the change. Moving a magnet toward a coil, moving the coil into a field, or switching a current on and off near the coil all produce an EMF as long as the flux changes.

Lenz's law and the minus sign

The minus sign in Faraday's law has a physical meaning, given by Lenz's law. The induced current flows in the direction that creates a magnetic field opposing the change in flux.

If you push the north pole of a magnet into a coil, the coil's induced current creates a north face that pushes back. You have to do work against that force, and the energy you spend appears as electrical energy in the circuit. If the rule were reversed, induction would create energy from nothing, which would violate conservation of energy.

Lenz's law explains why eddy currents slow down falling magnets in a metal tube. The changing flux induces currents in the tube, and those currents produce a magnetic drag force that opposes the fall.

A worked example

Consider a coil with 100 turns and area 0.01 m², placed perpendicular to a uniform magnetic field of 0.5 T. The field is switched off in 0.1 s.

1. Change in flux per turn: ΔΦ = B A − 0 = 0.5 × 0.01 = 0.005 Wb.
2. Rate of change: ΔΦ / Δt = 0.005 / 0.1 = 0.05 Wb/s.
3. Total induced EMF for 100 turns: EMF = 100 × 0.05 = 5 V.

The magnitude is 5 V. The sign tells you the current direction, which Lenz's law determines. A faster switch-off gives a larger EMF, which is why quick changes in magnetic field can produce sparks at switches in inductive circuits.

Generators

An electric generator is a coil rotating in a magnetic field. As the coil turns, the angle θ changes continuously, so the flux changes and an alternating EMF appears across the terminals. The output is sinusoidal when the rotation rate is constant.

Large power stations use steam or water to spin turbines, and the turbine drives a generator. The frequency of the grid, 50 Hz in Europe and 60 Hz in North America, equals the number of rotations per second times the number of pole pairs in the generator.

Bicycle dynamos and hand-crank radios work the same way, but on a much smaller scale. The faster the rotation, the faster the flux changes and the larger the EMF.

Transformers

A transformer uses two coils wound on a shared iron core. An alternating current in the primary coil creates a changing flux in the core. That flux passes through the secondary coil and induces an EMF there. Because the same flux links both coils, the voltages scale with the turn counts:

V_secondary / V_primary = N_secondary / N_primary

Power is conserved in an ideal transformer, so a step-up in voltage comes with a corresponding drop in current. Power lines run at high voltage to reduce resistive losses, which scale with the square of current. The step-down at the house end brings the voltage to a safe level.

The table below shows the turn ratios and output voltages for a 230 V primary.

Primary turns	Secondary turns	Ratio	Secondary voltage
1000	50	20 : 1 (step down)	11.5 V
1000	500	2 : 1 (step down)	115 V
100	1000	1 : 10 (step up)	2300 V

A transformer does not work with direct current. A steady current produces a steady flux, which induces no EMF in the secondary, so the principle requires a changing field.

Induction cooktops and wireless chargers

An induction cooktop places an alternating current in a coil beneath the glass. The changing magnetic field induces eddy currents in the iron base of a pan. The pan's own resistance turns those currents into heat, so the pan heats up while the glass stays cool.

Wireless phone chargers use the same idea across a small air gap. The transmitter coil creates a changing field, and the receiver coil in the phone induces an EMF that charges the battery. Efficiency drops quickly as the coils move apart, which is why charging pads must be placed close to the coil.

Where induction connects to other ideas

Induction ties together magnetism and electric fields. A changing magnetic field produces an electric field that circulates around it, and that electric field can drive charges round a loop. This is the integral form of Maxwell's equations, and it explains why light itself is a self-sustaining exchange of changing electric and magnetic fields.

Key takeaways

Electromagnetic induction produces an EMF whenever magnetic flux through a loop changes. Faraday's law sets its size, proportional to the rate of change of flux and the number of turns. Lenz's law sets its direction so that energy is conserved. Generators, transformers, induction cooktops and wireless chargers are all practical uses of this single principle, each arranging the changing flux in a different way.