Electromagnetic induction: drag a magnet through a coil and watch

How to use this simulation

1. Just let it go first: the magnet swings through the coil on its own and the galvanometer needle swings back and forth.
2. Grab the magnet and drag it yourself: pull it fast and the needle swings further than when you pull it slowly — e grows with the magnet's speed v.
3. Press "Flip the magnet": the needle now swings the opposite way, because the pole facing the coil has swapped.
4. Raise the number of turns, N: the emf reading grows in direct proportion to N — the table below shows the same thing.
5. Compare the two graphs on the right: wherever Φ is changing most steeply, e is largest at that exact instant — that is e = −N dΦ/dt, drawn out.

A bicycle dynamo, a wireless charger and a metal detector

Ride a bicycle at night and a small dynamo on the wheel spins a magnet next to a coil, and the headlamp lights up — no battery needed. That is exactly this simulation: a magnet moving near a coil changes the flux through it, and that change is what lights the lamp.

A phone charging wirelessly on a pad works on the same idea: two coils face each other, a rapidly changing current in one induces an emf in the other, with no wire between them. A metal detector finding a coin underground, an induction stove heating a pan directly, a guitar pickup turning a vibrating string into sound — all of it comes down to one fact: a changing magnetic flux creates an emf.

The two questions that matter are exactly how large that emf is, and which way the induced current flows. Those are Faraday's law and Lenz's law respectively. Grab the magnet in the simulation above and watch the galvanometer respond.

Starting from zero: magnetic flux and what "induced" means

How much magnetic field passes through a given area is called magnetic flux, symbol Φ. If the field B is perpendicular to the area A, then Φ = BA; if the field makes an angle θ with the perpendicular, Φ = BA cosθ. A coil of N turns links N times as much flux, called the flux linkage, NΦ.

Here is the key idea: flux by itself does nothing. A magnet sitting perfectly still inside a coil produces a large flux but no emf whatsoever. An emf appears only when the flux changes with time — the magnet moves, its strength changes, or the coil turns. This whole phenomenon, an emf appearing because flux is changing, is electromagnetic induction, and the emf it produces is the induced emf.

The English scientist Michael Faraday discovered this in 1831. He moved a magnet near a coil connected to a galvanometer and saw the needle move — but only while the magnet was actually moving. Hold it still and the needle stops. The American scientist Joseph Henry observed essentially the same effect independently around the same time. This one observation is the seed of every generator, transformer and power station running today.

In the simulation, hold the magnet perfectly still (stop dragging it and pause the auto-swing): the needle sits dead centre at zero. It responds only once the magnet starts moving again.

Key terms in electromagnetic induction

Get the vocabulary straight first; definition questions in exams come straight from this table.

Faraday's law: e = −N dΦ/dt

Faraday's law of electromagnetic induction states that the emf induced in a coil is proportional to the rate of change of flux linkage, and opposite in sign to it: e = −N dΦ/dt. Here dΦ/dt is how quickly the flux per turn is changing, and multiplying by N scales it up to the whole coil's induced emf.

Three consequences follow directly. First, a faster-changing flux (pulling the magnet quickly, or spinning it faster) gives a larger e. Second, more turns N means the same rate of flux change produces proportionally more total e — try changing the turns slider in the simulation to see this directly. Third, the flux itself does not need to be large, only changing: a weak magnet moved quickly can beat a strong magnet held still, which gives exactly zero emf.

In exam problems dΦ/dt is often written as the average rate ΔΦ/Δt, when the flux changes at a steady pace. Most of the worked problems below use this average form, since school-level problems almost always assume a steady rate of change.

Lenz's law: what the minus sign actually says

The minus sign in Faraday's law is not decoration; it is Lenz's law: the induced current always flows in whichever direction opposes the very change in flux that produced it. As the magnet approaches, flux is increasing, so the induced current creates a magnetic field that opposes that increase — the coil's near face develops the same pole as the magnet's leading pole, so like poles repel and the coil resists the approach.

As the magnet moves away, the opposite happens: flux is decreasing, so the induced current now creates a pole opposite to the magnet's trailing pole, so opposite poles attract and the coil tries to pull the magnet back. That is exactly why the simulation shows one pole label as the magnet comes in and the opposite one as it leaves — the coil is always fighting whatever the magnet is doing.

Lenz's law is really a statement of energy conservation. If it worked the other way round — the induced current helping the magnet along instead of opposing it — the magnet would accelerate on its own, generating energy from nothing, which never happens. That is why you have to push the magnet to move it against the coil's opposition, and the work you do against that opposition is exactly the electrical energy you get out.

Try these experiments in the simulation

Predict what will happen before each experiment, then check.

• Drag the magnet very slowly across, then drag the same path very fast. How much further does the needle swing when you go fast?
• Press "Flip the magnet" and repeat the same drag speed. Which way does the needle swing now, compared with before?
• Double the number of turns, N, keeping everything else the same. Does the emf reading really double?
• Turn magnet strength all the way down, then all the way up. How does the height of the peak on the Φ–t graph change?
• Hold the magnet perfectly still right at the coil's centre. Φ is still large there — so why does e read zero?
• Set the oscillation speed to its slowest. Does the e–t graph look flatter or steeper than before?

Solved problems

Every solution states what is given, then the formula, then the substitution — write it this way in exams to get full marks.

How the induced emf scales with the number of turns

Holding the rate of flux change fixed (here 5.0 mWb/s), e grows in direct proportion to N, because N multiplies the rate directly in the formula. Try the turns slider in the simulation to check this proportionality yourself.

Common mistakes

Avoiding these keeps marks safe on both the numeric and the conceptual questions.

• Thinking a large flux by itself gives a large emf. What matters is the rate of change; a huge but unchanging flux gives e = 0.
• Dropping the minus sign, or treating it as decoration. That sign is Lenz's law — it tells you the direction of the induced current.
• Confusing flux Φ (per turn) with flux linkage NΦ (the whole coil). A coil's total induced effect scales with N, not just Φ.
• Applying e = BLv without checking the condition. It only holds when the field, the rod's length and its velocity are all mutually perpendicular.
• Treating motional emf (e = BLv) and Faraday's general law (e = −N dΦ/dt) as two unrelated formulas. They describe the same physics from two different bookkeeping angles.
• Assuming eddy currents are always a nuisance. They waste energy in a transformer core, but the very same eddy currents are exactly what makes an induction stove or an eddy-current brake work.
• Assuming the needle keeps deflecting the same way forever. The moment the magnet passes through and starts receding, the deflection reverses.

Real-life uses of electromagnetic induction

This single principle sits underneath most of the modern electrical world, well beyond the exam.

• Power-station generators: a turbine spins a coil or magnet, changing flux and producing enormous induced emfs.
• Transformers: a changing flux in one coil induces an emf in a neighbouring coil, stepping voltage up or down by the ratio of turns.
• Wireless charging: a changing magnetic field between two coils carries energy across with no wire at all.
• Induction cooktops: a rapidly changing field induces eddy currents directly in the base of the pan, heating the metal itself.
• Metal detectors and contactless cards: a changing field induces a current in nearby metal or in a chip, which sends back a signal.
• Regenerative braking in electric cars: the motor is run as a generator while slowing down, turning kinetic energy back into stored charge.
• Guitar pickups and some microphones: a vibrating string or diaphragm changes the flux through a nearby coil, turning motion into an electrical signal.

Exam corner

Electromagnetic induction is a staple topic across school and college physics: expect a statement-and-derive question on Faraday's and Lenz's laws, a conceptual question on why the minus sign matters, and a numeric question using e = −N dΦ/dt or e = BLv.

Revision: the one-screen summary

This list and the table above are all you need the night before an exam.

• Electromagnetic induction: an emf appears whenever flux through a coil changes. Flux alone is not enough — it must change.
• Faraday's law: e = −N dΦ/dt, or e = −N ΔΦ/Δt for a steady rate of change.
• Lenz's law: the induced current always opposes its own cause — repelling an approaching magnet, attracting a receding one.
• Motional emf: e = BLv, when B, L and v are mutually perpendicular.
• Peak emf of a rotating coil: e₀ = NBAω.
• e is proportional to both N and dΦ/dt; flux linkage = NΦ.
• Eddy currents: induced swirling currents inside a solid conductor — wasteful in a transformer core, useful in an induction stove.

Frequently asked questions