Φ = B·A·cosθ · ε = −N·ΔΦ/Δt · Lenz's law · the generator
Hold a magnet still inside a coil and the meter reads zero. Move it so the flux through the coil changes, and an EMF appears — close the circuit and a current flows. What the coil answers to is not the field, and not the movement. It is the change in what it catches.
This page covers magnetic flux, Faraday's law ε = −N·ΔΦ/Δt, the moving-rod form ε = Blv, Lenz's law, and the generator that turns all of it into power. By the end you'll be able to:
Almost all the electricity you have ever used came from a coil turning near a magnet. Boards test this twice — once as the generator in Class 10, once as the full law in Class 12:
Searched as: faraday's law, electromagnetic induction, induced emf formula, lenz's law, magnetic flux, ac generator, motional emf.
Predict the peak EMF, lock it, then push the magnet through at different speeds and turns. Flux · ε = −N·ΔΦ/Δt · Lenz sign. 🟢 real flux engine
Guess, then push the magnet — the meter waits until you commit.
Set the speed, the turns and the magnet — then watch what the coil does with the change.
Flux is B·A·cosθ. Before asking whether there is an EMF, name which of those three moved. Six situations — your answers build the table underneath.
A magnet is pushed towards a still coil. What changed?
Read the picture, then name the one that changed.
The question is never whether something is moving. It is what changed in B·A·cosθ.
The coil has 200 turns and the magnet is fixed at 200 mT. Dial the speed so the peak EMF lands on the amber target — 3 attempts.
Pick a speed, then push. The peak EMF comes straight from ε = −N·ΔΦ/Δt.
Each setup breaks the law somewhere. Tap the broken idea. Expert thinking starts when something looks almost right.
No change in flux means no induced EMF, and a magnet at rest holds the flux constant — so the reading is zero. Note the rule is about the flux, not the motion: a coil that never moves still shows an EMF if the field around it is changing.
That would pull the magnet in, speed it up, and make more current from nothing. Lenz's law exists to forbid exactly this.
Faraday's law is about ΔΦ/Δt. Drop the time and the units alone tell you it is wrong — webers are not volts.
Thinking beats memorising. Sort every induction situation into three boxes.
Read the motion, then decide what the near face of the coil must become. Lenz's law has only one rule and it never bends.
A pole coming closer is met by the same pole. A pole leaving is held back by the opposite one.
Pick a job. Dial the turns, the magnet and the spin. The formula tells you whether you built the right machine.
Peak EMF is N × B × A × ω, with the coil area fixed at 0.01 m².
No equipment needed — read the scene. What is changing, and what is answering?
The coil's changing field makes currents inside the steel base. The heat is born in the pan, so the glass never has to carry it.
The card carries a flat coil around its edge. Held in a changing field, it gets just enough induced current to run its chip for a moment.
Copper is not magnetic at all. The falling magnet changes the flux through each ring of pipe, and the currents that appear push back — Lenz, working as a brake.
In plain terms: a coil keeps count of how much magnetic field passes through it. It reacts only when that count changes — by any route at all — and it reacts in the direction that makes the change harder.
Magnetic flux is how much field a loop catches: Φ = B·A·cosθ. A wide loop catches more. A strong field gives more. Turn the loop edge-on to the field and it catches nothing at all. The unit is the weber, and one weber is one tesla across one square metre.
Flux is B·A·cosθ, so anything that changes B·A·cosθ changes the flux — that single sentence is the whole cause. Three changes cover most of what you will meet: change B (a transformer switching on), change θ (a generator turning its coil), or change where the loop sits in an uneven field (your hand with a magnet). A sliding rod reveals the fourth view: it changes A, the area the circuit encloses. Do not ask whether something is moving. Ask what changed in B·A·cosθ.
The induced current always flows the way that opposes the change in flux that made it — not the motion itself, which only happens to be the cause in most school examples. Push a north pole in and the coil shows you a north face. Pull it out and the coil shows a south face to hold it back. Switch on a nearby electromagnet and the coil opposes the rising flux although nothing has moved at all. This is not politeness — it is energy conservation. If the coil helped instead, you would get current and acceleration for free.
An open coil still has an EMF but no current — the push is there with nowhere to go. A coil turned edge-on and spun through the field position gets its biggest EMF exactly where the flux is momentarily zero, because that is where flux changes fastest. And a solid sheet of metal needs no winding at all: the currents simply go round in loops inside it.
Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.
Three small labs, each one native to this law. Drag, and watch which number moves.
Six wrong ideas that survive because they sound sensible. Tap a card to bust the myth.
Michael Faraday wound one coil to a battery through a switch and the other to a meter. The needle jumped only when he opened or closed the switch — never while the current ran steadily. Change, not current, was doing it.
Within weeks he was turning a copper disc between the poles of a magnet and drawing a steady current off it. A machine that made electricity from motion, built out of a hunch about change.
Heinrich Lenz stated the rule that fixes which way the induced current flows: it opposes the change that made it. Faraday had the size; now the law had its sign, and with it, energy conservation.
Westinghouse and Tesla built generating and transformer systems on exactly this principle, and the argument over whether power should alternate was settled by how cheaply it could be carried.
Steam, water, wind and diesel all end the same way: something spins a coil near a magnet. The twitch of Faraday's needle is now the last step in nearly all the electricity on earth.
A turbine spins a coil between magnets. Steam, water and wind differ only in what does the spinning — the last step is always this law.
Two coils a few millimetres apart. One carries a changing current, the other picks up the EMF, and no metal ever touches.
Move a magnet past a rail and eddy currents appear in it. They push back, the train slows, and no brake pad wears out.
One sentence each: what changes, and what answers.
Drag the slider. Same law, six machines, voltages from three to twenty thousand.
The machine grows; the sum stays the one you just did by hand.
Physics you can see on a table. Each one is a build and a measurement — the measuring is what turns a demo into a project.
Build: wind 100 turns of thin wire round a pen, connect the ends to a cheap multimeter on its most sensitive DC setting.
Measure: the reading while the magnet is moving, and while it rests inside. One of them is zero.
Build: drop the same magnet through the same coil from five different heights.
Measure: peak reading each time; plot it against √h, which is the entry speed.
Build: drop a small neodymium magnet down a copper pipe, and a steel ball of the same mass beside it.
Measure: time both falls. The difference is the energy the induced currents took.
Build: a coil on a spindle between two magnets, turned by a cotton reel and a string.
Measure: turns per second against volts. The graph should be a straight line through the origin.
Build: wind two separate coils on one nail; one to a battery through a switch, one to a meter.
Measure: when the needle moves. Only at switch-on and switch-off — Faraday's own 1831 result.
Build: four coils on identical tubes with 50, 100, 200 and 400 turns.
Measure: drop the same magnet through each from the same height; plot peak volts against turns.
Straight answers, each one complete on its own:
The EMF induced in a coil equals the number of turns multiplied by the rate at which the magnetic flux through it changes: ε = −N·ΔΦ/Δt. Flux is measured in webers, time in seconds, and the result is in volts. The minus sign records the direction, not the size.
Because the law depends on the rate of change of flux, not on flux itself. A stationary magnet gives a constant flux, so ΔΦ/Δt is zero and the EMF is zero. A very strong magnet held perfectly still induces nothing at all, which is the single most useful fact in the chapter.
It states Lenz's law: the induced current flows in whichever direction opposes the change that created it. Push a north pole towards a coil and the coil's near face becomes north, pushing back. If it attracted instead, the magnet would accelerate on its own and produce energy from nothing.
An EMF is a push, and a push needs a complete path before anything moves. Break the circuit and the voltage still appears across the open ends, measurable with a voltmeter, while the current stays at zero. Close the loop and I = ε/R decides how much flows.
Flux is B·A·cosθ, so any change in one of those three changes it. B changes when a transformer switches on or a magnet comes nearer. θ changes when a generator turns its coil. A changes when a rod slides and the circuit encloses more area. The useful question is never whether something is moving — it is which of B, A or θ has changed.
None in principle. ε = B·l·v is the same law applied to a straight conductor sliding across a field: as it slides it sweeps out area, the flux through the circuit changes, and an EMF appears. The rod version is quicker to use when the geometry is simple.
A transformer needs the flux in its core to keep changing. Alternating current reverses fifty times a second, so it never stops changing. Steady direct current produces a steady flux, the rate of change is zero, and the secondary coil gives nothing — except at the instants of switching on and off.
From whatever is doing the moving. The induced current creates a magnetic field that drags on the magnet, so your hand, the turbine or the falling water has to work harder. Stop pushing and the current stops. Every joule that comes out of the coil went in as mechanical work first.
Spot these before the exam does.
Seven question formats, the way LLOS.ai serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
Four coils, no numbers yet. Tap them in order, biggest EMF first. Then read what the law actually gives — and see what fooled you.
A very strong magnet, eased through a 200-turn coil so slowly you could time it with a calendar.
A weak fridge magnet, thrown through the same 200-turn coil as fast as your hand can move.
An ordinary magnet at an ordinary speed, through a coil wound with 800 turns.
The strongest field in the room, a 500-turn coil, and absolutely nothing moving.
Tap the four in the order you believe, strongest first.
A magnet lying still in a coil is worth nothing. Every volt in every power station is paid for by something that had to keep moving.