Electromagnetic Induction: Faraday's Law Explained

What is electromagnetic induction?

Electromagnetic induction was discovered by Michael Faraday in 1831. He wound two coils on an iron ring and noticed that a current flashed in one coil only at the moment the current in the other was switched on or off. The same happens with a bar magnet and a coil: the voltage appears while the magnetic field is changing, not while it is steady.

Two ideas matter:

• Magnetic flux (Φ): the amount of magnetic field passing through a loop, measured in webers (Wb). It is Φ = B × A × cos θ, where B is the field strength in tesla, A is the area in square metres, and θ is the angle between the field and the loop's normal.
• Induced emf: the voltage made by a changing flux, measured in volts (V).

Faraday's law explained: what does it say?

Faraday's law says that the induced emf equals the rate of change of magnetic flux linkage:

emf = −N × ΔΦ / Δt

where N is the number of turns in the coil, ΔΦ is the change in flux (Wb) and Δt is the time taken (s).

So you can raise the induced voltage in three ways:

1. Move the magnet faster (a smaller Δt).
2. Use a stronger magnet (a larger B).
3. Use more turns of wire (a larger N).

Worked example. A coil with 200 turns has its flux change from 0 to 0.004 Wb in 0.5 s. The emf is 200 × 0.004 ÷ 0.5 = 1.6 V. Double the speed, so the same change takes 0.25 s, and the emf doubles to 3.2 V.

What does Lenz's law say?

Lenz's law gives the direction of the induced current: it always flows so that its own magnetic field opposes the change that caused it. That is the meaning of the minus sign in Faraday's law.

Push the north pole of a magnet towards a coil. The coil's induced current makes its near face a north pole too, which pushes back on the magnet. Pull the magnet away and the coil makes a south pole to attract it back. You have to do work against this force, and that work is the energy that ends up in the electrical current. Lenz's law is the conservation of energy applied to induction: without the opposing force, you could get free energy.

How does a generator work?

A generator turns a coil in a magnetic field, or a magnet inside a coil. As the coil rotates, the angle θ changes, so the flux through it keeps changing and an emf is induced. The output is an alternating current that rises, falls and reverses direction, once per turn of a simple one-coil generator.

The emf is biggest when the coil's sides cut straight across the field lines and zero when they move along them. More turns, a stronger field and a faster rotation all increase the peak voltage. In a power station, steam, water or wind turns the coil or magnet.

How does a transformer use induction?

A transformer has two coils wound on one iron core. An alternating current in the primary coil makes a changing magnetic flux in the core. That flux passes through the secondary coil and induces an alternating emf there. The voltages follow the turns ratio:

Vs / Vp = Ns / Np

A transformer with 100 turns on the primary and 1,000 on the secondary raises 230 V to 2,300 V. Power grids step voltage up for transmission, because a high voltage means a lower current and less energy lost as heat in the cables, then step it down for homes. Transformers only work with AC, because a steady DC makes no changing flux.

Common mistakes with induction

• Thinking a steady magnetic field induces a current. Only a changing flux does. A magnet at rest inside a coil produces nothing.
• Ignoring the minus sign. It is not just maths: it tells you the induced current opposes the change.
• Forgetting the number of turns. The emf scales with N, so a 500-turn coil gives ten times the emf of a 50-turn coil.
• Mixing up emf and current. Faraday's law gives the emf (volts). The current also depends on the circuit's resistance, from Ohm's law.
• Expecting a transformer to create energy. A step-up transformer raises voltage but lowers current, so output power cannot exceed input power.

Frequently asked questions

What is electromagnetic induction in simple words?

Electromagnetic induction is making electricity by changing a magnetic field around a wire. If a magnet moves near a coil, a voltage is induced in the coil. The voltage lasts only while the magnetic field through the coil is changing.

What is the difference between Faraday's law and Lenz's law?

Faraday's law tells you how big the induced emf is: it equals the number of turns times the rate of change of flux. Lenz's law tells you its direction: the induced current opposes the change that made it. Together they give the full picture.

How can you increase the induced emf?

You can move the magnet or coil faster, use a stronger magnet, or add more turns of wire to the coil. Each of these makes the flux linkage change faster, which raises the emf. Doubling the speed doubles the emf.

Why does a magnet fall slowly through a copper tube?

The falling magnet changes the flux through the tube, which induces circular currents called eddy currents. By Lenz's law, those currents make a magnetic field that opposes the magnet's motion, so it falls much more slowly than a magnet in free fall.

Where is electromagnetic induction used?

It is used in power station generators, transformers, induction cooktops, wireless phone chargers and electric guitar pickups. In each, a changing magnetic field induces a voltage or heating current in a nearby conductor.

Try it yourself

Open the Electromagnetic Induction tool and move the magnet in and out of the coil. Watch the meter jump while the magnet moves and settle to zero when it stops. Then move it faster and add more turns to see the emf rise. To see how voltage and current are linked, read Ohm's law explained and conservation of energy examples.