Faraday’s law told you how big an induced e.m.f. is. It said nothing about which way the current flows. Lenz’s law fills that gap with one deceptively simple idea: the induced current always fights back. Push a magnet at a coil and the coil pushes back at the magnet. Pull it away and the coil tries to drag it back. Nature refuses to give you electrical energy for free — and that stubbornness is just the conservation of energy in disguise.
📘 What you need to know
Lenz’s law predicts the direction of an induced e.m.f. or current
It states: the induced e.m.f. is such that it opposes the change causing it
It is a direct consequence of the conservation of energy
Combined with Faraday’s law it gives ε = −NΔΦ / Δt — the minus sign is Lenz’s law
The induced current creates its own magnetic field that opposes the change in flux
A magnet’s north pole approaching a coil induces a north pole facing it (they repel)
A magnet leaving the coil induces a pole that attracts it, trying to pull it back
Work must be done against this opposing force — that work becomes the electrical energy
The current direction can be found with the right-hand grip rule
The law in one line
Lenz’s law is short enough to memorise word for word — and examiners want it word for word:
The induced e.m.f. is such that it opposes the change causing it.
Stitch it onto Faraday’s law and the opposition shows up as a minus sign:
Faraday’s law with Lenz’s lawε = −NΔΦ / Δtthe minus sign means the e.m.f. drives a current that fights the change in flux
The minus sign isn’t decoration — it is Lenz’s law. Strip it off and you’re left with plain Faraday, which only gives the size. Put it back and you’re saying “and it points the way that resists”. If a question ever asks you to explain the negative sign in the induction equation, “it represents Lenz’s law / conservation of energy” is the mark.
Pushing a magnet into a coil
Here’s the classic demonstration. Push the north pole of a bar magnet toward a coil connected to a sensitive ammeter. As the magnet moves in, the flux through the coil grows — a change — so a current is induced. Which way?
Lenz says the coil must oppose the incoming magnet. The only way to oppose an approaching north pole is to greet it with an induced north pole, because two norths repel. So the induced current flows in whatever direction makes the coil’s near face a north pole.
Push a north pole in and the coil answers with its own north pole to repel it. That opposition is Lenz’s law in action — and it’s why you feel resistance as you push.
Reverse everything and the logic flips neatly:
What you do
Flux change
Coil’s near face
Effect on magnet
Push N pole in
Increasing
Becomes N
Repels it (fights entry)
Pull N pole out
Decreasing
Becomes S
Attracts it (fights exit)
A single sentence captures both rows: the coil always tries to keep things the same. Magnet coming in? It pushes back to keep it out. Magnet leaving? It pulls to keep it in. The induced current is nature’s way of saying “please don’t change the flux” — and losing every time, but never without a fight.
Why it must be true: conservation of energy
Imagine Lenz’s law ran backwards — that the coil attracted an incoming magnet instead of repelling it. The magnet would accelerate in on its own, inducing a current, which would generate heat and light… all from nothing. You’d have a free energy machine. Physics forbids it.
Push magnet (do work)
against the repulsion
Induced current
dissipates as
Electrical / heat energy
Because the coil opposes the motion, you must do work to keep pushing. That work is exactly the electrical energy that appears in the circuit. Energy in equals energy out — the books balance, and they only balance if the induced current opposes the change.
WE 1
The north pole of a bar magnet is pushed toward a coil connected to a sensitive ammeter. (a) State the polarity induced on the near face of the coil, and explain why. (b) State and explain what happens to the ammeter reading if the magnet is then pulled away faster than it was pushed in.
(a) polarity of the near face
The flux through the coil is increasing, so by Lenz’s law the coil opposes it.
To oppose an approaching north pole it must repel it.
the near face becomes a north pole(b) pulling away faster
The flux now decreases, so the current reverses — the needle deflects the other way.
Pulling faster means a bigger rate of change of flux.
a larger deflection, in the opposite directionTwo things change at once here: the direction flips (because the flux now falls instead of rises) and the size grows (because it’s faster). Keep the two effects separate in your answer and you’ll bag both marks.
Finding the current direction
Once you know which pole the coil must show, the right-hand grip rule gives the current direction: point your right thumb along the way the field must point inside the coil (out of the north face), and your curled fingers show the way the current circulates.
Thumb along the field (out of the north face), fingers curl the way the current flows. Get the required pole from Lenz’s law first, then let your right hand do the rest.
WE 2
A coil of 150 turns experiences a steady change in magnetic flux of 4.0 mWb over 0.20 s as a magnet is pushed in. (a) Calculate the magnitude of the induced e.m.f. (b) The coil has resistance 6.0 Ω and is part of a complete circuit. Calculate the induced current. (c) State where the energy dissipated in the coil comes from.
(a) Step 1 — magnitude from Faraday’s law|ε| = NΔΦ/Δt = 150 × (4.0 × 10⁻³) / 0.20|ε| = 3.0 V(b) Step 2 — current from V = IRI = ε/R = 3.0 / 6.0I = 0.50 A(c) where the energy comes fromfrom the work done pushing the magnet against the coil’s opposing forcePart (c) is the heart of Lenz’s law: the electrical energy isn’t free. It’s paid for by whoever is pushing the magnet, doing work against the repulsion. Take away the push and the current — and the energy — stops.
WE 3
Two coaxial conducting loops X and Y face each other. A steady current flows in X, and loop Y is moved towards X at constant speed. (a) State how the flux through Y changes. (b) State and explain the direction of the induced current in Y relative to X’s current. (c) Explain why work must be done to keep Y moving at constant speed.
(a) flux through Y
As Y approaches X it sits in a stronger part of X’s field.
the flux through Y increases(b) direction of Y’s current
By Lenz’s law, Y opposes the increasing flux.
Its induced current makes a field that opposes X’s field between them.
Y’s current flows opposite to X’s — the loops repel(c) why work is needed
The loops repel, so moving Y closer means pushing against a force.
work is done against the repulsion, and it becomes the electrical energy in YOpposite currents in parallel wires (or loops) repel — that’s the link back to the forces topic. Lenz’s law and the motor-effect force are two sides of the same coin here.
🧲 Working a Lenz’s-law direction question
Is the flux rising or falling? Magnet approaching → rising; leaving → falling.
The coil opposes it. Rising flux → repel (same pole faces the magnet); falling → attract.
Name the near-face pole the coil must show.
Right-hand grip rule: thumb out of the N face, fingers give the current direction.
Energy check: the induced current always opposes the motion, so work is done.
Sign: the minus in ε = −NΔΦ/Δtis Lenz’s law.
💡 Top tips
Learn the statement word for word: the induced e.m.f. opposes the change causing it.
The minus sign in the induction equation is Lenz’s law — know that if asked.
Use the right-hand grip rule to turn the required pole into a current direction.
Lenz’s law = conservation of energy. If asked “why”, that’s the answer.
Work is always done against the induced effect — that’s the source of the electrical energy.
⚠ Common mistakes
Saying the coil attracts an approaching magnet — it repels to oppose the change
Forgetting the minus sign represents Lenz’s law, not just a maths artefact
Thinking the induced current appears “for free” — it’s paid for by work done
Using the same current direction whether the magnet enters or leaves — they’re opposite
Confusing Lenz’s law (direction) with Faraday’s law (size) — you usually need both
Mixing up the right-hand grip rule with Fleming’s left-hand rule
Quick recap:Lenz’s law gives the direction of an induced current: it always opposes the change causing it, which is why the induction equation carries a minus sign, ε = −NΔΦ/Δt. A magnet pushed in meets an induced like pole (repulsion); a magnet pulled out meets an opposite pole (attraction). Find the required pole, then use the right-hand grip rule for the current. It’s all a consequence of the conservation of energy: work done against the opposing force becomes the electrical energy in the circuit.
Everything so far — induced e.m.f., flux, Faraday, Lenz — comes together in one wonderfully useful machine. Spin a coil steadily in a magnetic field and the flux linkage rises and falls smoothly, so the induced e.m.f. swings positive and negative over and over. That’s alternating current, and the device that makes it is the AC generator. Next page: AC Generators.
Lenz’s law leaving you turned around?
Book a free meeting and we’ll nail the “oppose the change” rule, the pole logic, and why the minus sign is really conservation of energy.
