Electromagnetic Induction
Push a bar magnet into a coil of wire and a needle on a meter flicks. Pull it out and the needle flicks the other way. No battery, no chemistry — just motion and magnetism conjuring a voltage. This is electromagnetic induction, the discovery that powers almost every electrical generator humanity has ever built.
The core observation
Michael Faraday found in 1831 that a changing magnetic environment around a circuit drives a current through it. The crucial word is changing. A magnet sitting motionless inside a coil produces nothing. It is only while the magnetic field through the coil is increasing or decreasing that a voltage — called an electromotive force, or EMF — appears.
To make this precise we need a way to measure “how much magnetic field passes through the coil”. That quantity is magnetic flux.
Magnetic flux
Magnetic flux Φ counts the number of magnetic field lines threading a loop. For a uniform field B passing through a flat area A at angle θ to the surface’s normal direction:
Flux is measured in webers (Wb). You can increase the flux through a coil three ways: make the field stronger, make the area larger, or rotate the loop so it faces the field more squarely. Change any of these over time and you have induction.
It is not the magnetic field that induces a voltage, but the rate of change of the flux through the circuit. A constant flux, however large, induces nothing.
Faraday’s law
Faraday’s law turns the observation into an equation. For a coil of N turns, the induced EMF equals the number of turns multiplied by how fast the flux is changing:
The minus sign is Lenz’s law, explained below. The size of the EMF tells you that to get a big voltage you can use many turns, a strong magnet, or rapid motion. A bicycle dynamo spinning quickly produces more light than one turning slowly, because Δt shrinks and the EMF grows.
Lenz’s law and the direction of the current
The minus sign encodes a deep principle: the induced current always flows in the direction that opposes the change that created it. Push a magnet’s north pole into a coil and the coil’s near face becomes a north pole too, pushing back against you. Pull the magnet away and the coil turns into a south pole, trying to drag it back.
This is not the universe being awkward — it is conservation of energy in action. If the induced current helped the motion, you would get free kinetic energy. Instead you must do work against the opposing force, and that work is exactly the electrical energy you generate. This same idea underlies conservation of energy throughout physics.
Generators and everyday induction
A generator is a coil rotating in a magnetic field. As it spins, the angle θ between the coil and the field changes continuously, so the flux rises and falls smoothly, producing an alternating EMF shaped like a sine wave:
Here ω is the angular speed of rotation. Spin faster and both the frequency and the peak voltage increase. Almost all grid electricity — from coal, gas, nuclear, hydro and wind — comes from spinning a coil or magnet exactly this way.
- Transformers use a changing current in one coil to induce a voltage in another, stepping voltages up or down.
- Induction cooktops induce swirling currents directly in the metal pan, heating it without a flame.
- Microphones and electric guitar pickups turn vibrations near a coil into electrical signals.
Motional EMF: a second viewpoint
You can also induce a voltage by moving a conductor through a field rather than changing the field itself. A rod of length L sliding at speed v perpendicular to a field B develops a voltage across its ends:
Physically, the field pushes the free charges in the moving rod sideways, piling them up at the ends. This is fully consistent with Faraday’s law: as the rod slides, it sweeps out new area, so the flux through the circuit changes. Both pictures give the same answer, which is one of the quiet beauties of electromagnetism.
Frequently asked questions
Does a stationary magnet ever induce a current?
No. As long as nothing changes — the magnet, the coil, and their positions all held still — the flux is constant and the induced EMF is zero. Induction requires change.
Why is there a minus sign in Faraday’s law?
It represents Lenz’s law: the induced current opposes the change in flux that produced it. This guarantees energy conservation, since you must do work to drive the current against the opposing force.
How is this different from a battery?
A battery uses chemical reactions to separate charge and maintain a steady voltage. Induction uses a changing magnetic flux to drive charge, and naturally produces alternating voltages when a coil rotates in a field.
