Lenz's Law — Why Induced Current Opposes Change
Lenz's law: why induced current always opposes the change in magnetic flux, how it enforces energy conservation, eddy currents, and worked flux-change examples.
Quick answer
Lenz's law says the current induced by a changing magnetic flux always flows in the direction that opposes the change. Push a magnet toward a loop and the induced current makes the loop push back; pull it away and the loop pulls back.
Unit: induced emf ε in volts (V); flux Φ in webers (Wb)
Example: A magnet's north pole approaches a loop, raising the flux by 4.0×10⁻⁴ Wb in 0.10 s: emf = −ΔΦ/Δt = −4.0 mV (the minus sign is Lenz's law), driving a current whose field opposes the approach.
What you will learn
- State Lenz's law in words and identify the minus sign in Faraday's law
- Predict induced-current direction for approaching and receding magnets
- Explain how Lenz's law enforces conservation of energy
- Describe eddy currents and one practical use
- Work a flux-change example quantitatively
The law of opposition
Faraday's law says a changing magnetic flux induces an emf: . The magnitude is Faraday's; the direction is Lenz's. In plain words:
> Lenz's law: the induced current flows so that its own magnetic field opposes the change in flux that created it.
Push a north pole toward a loop → flux through the loop rises → the induced current makes the loop's near face a north pole, repelling the magnet. The universe pushes back against the change. Pull the magnet away → flux falls → the current flips, making a south pole that tries to hold the magnet back. Either way, the induced effect fights the change — never the field itself.
Why the minus sign is mandatory
Why must nature behave this way? Follow the alternative. Suppose the induced current helped the change: pushing a magnet toward a loop would induce a current that attracts the magnet, pulling it in faster, inducing more current, pulling harder — a runaway that manufactures kinetic energy and electrical energy from nothing.
Lenz's law forbids exactly that. The repulsion you feel when pushing the magnet in is you doing work against the induced field — and that work is precisely the energy that appears as electrical energy in the loop. The minus sign is conservation of energy, not a sign convention. Every generator obeys it: turning the crank gets harder the more current you draw, because the induced current always opposes the motion producing it.
Opposition costs work, and that work is where the electrical energy comes from. No opposition → no energy bill → perpetual motion. Lenz's law is the universe insisting the bill gets paid.
A three-step direction recipe
A systematic way to get the direction right every time:
- Find the change. Is the flux through the loop increasing or decreasing? (Magnet approaching = increasing; receding = decreasing; area shrinking in a steady field = decreasing.)
- Decide what field the loop wants. Increasing flux → the induced current makes a field opposing the external field. Decreasing flux → it makes a field supporting the external field.
- Curl your right-hand fingers around the loop with your thumb along that desired field direction — your fingers show the current direction.
Note step 2's subtlety: for decreasing flux, Lenz's law has the loop reinforce the original field. Beginners who memorize 'oppose the field' get this case backwards — always oppose the change.
Eddy currents: Lenz's law in bulk metal
A changing flux does not need a neat loop of wire. In any chunk of conductor — a spinning metal disk, a magnet dropped through a copper pipe — the induced emf drives swirling eddy currents.
Because eddy currents always oppose the change (Lenz), they act as a brake on the motion causing them: the falling magnet induces currents whose field repels it, so it drifts down slowly instead of dropping. Roller coasters and some trains use this as a frictionless brake — no pads, no wear, nothing to overheat except the conductor itself.
The flip side is waste: eddy currents in transformer cores turn electrical energy into useless heat. Engineers laminate cores from thin insulated sheets, breaking the swirls into tiny, weak loops — Lenz's law tamed by geometry.
Worked example: growing field, opposing current
A single loop of area sits in a uniform field perpendicular to its plane. The field strengthens from to in . Find the induced emf and state the current's direction relative to the field.
Flux change: .
Emf: .
Direction: flux is increasing in the direction of B, so the induced current creates a field pointing opposite to B. By the right-hand rule, the current circulates so that its thumb points against the external field — opposing the increase, exactly as Lenz demands.
The negative emf is not 'negative voltage' in any absolute sense — it is the math's way of saying the induced field points opposite the flux change. If the field had been weakening instead, the same calculation would give a positive emf: current reinforcing the field.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Induced emf | V | Induced electromotive force | |
| Turns | dimensionless | Number of turns in the coil | |
| Magnetic flux | Wb | Magnetic flux through the loop(s) | |
| Flux change rate | Wb/s = V | Rate of change of flux | |
| Time interval | s | Time over which the change happens |
Common mistakes
It opposes the change in flux, not the field. If flux through a loop is decreasing, the induced current tries to reinforce the field — supporting it, not fighting it.
It is physics, not bookkeeping: it encodes energy conservation. Flip it and you get perpetual motion — the induced current would amplify its own cause without any energy input.
They dissipate energy as heat only in resistive conductors (eddy-current heating). In a superconducting loop, induced currents persist indefinitely with no loss — opposition without dissipation.
Real-world applications
Induction cooktops heat the pan (not the stove) because Lenz's law forces the induced currents to oppose the coil's changing field — dumping energy as heat in the metal.
Drop a magnet through a copper tube and it falls in slow motion: induced currents brake it, a favorite lecture demo of Lenz's law.
Eddy-current brakes stop roller coasters and trains without any touching parts — the motion itself induces the braking force.
Metal detectors and guitar pickups both read the tiny opposing fields that induced currents generate.
Frequently asked questions
Is Lenz's law the same as Faraday's law?
It is not a separate force law — it is the minus sign in Faraday's law, ε = −N·dΦ/dt. Faraday tells you the size of the induced emf; Lenz tells you its direction: always opposing the change that produced it.
If I push a magnet into a coil, does the coil attract or repel it?
Repulsion. Pushing the north pole toward the loop increases the flux through it, so the induced current makes the near face a north pole to push back. That is the 'opposition' made visible — you feel yourself doing the work.
What would happen if Lenz's law were reversed?
Then energy would come from nothing: the induced current's field would strengthen the change, inducing more current, forever — a runaway that creates energy out of nowhere. Lenz's law is conservation of energy wearing a magnet costume.
A strong magnet sits still inside a coil. What is induced?
Zero. No change in flux means no emf, no matter how strong the field is. A huge steady field induces nothing — only change counts. Motion, rotation, or a varying field are all ways to get change.
Does Lenz's law still apply if the loop has almost no resistance?
Short the loop with a wire of tiny resistance and the current can be large — that is exactly what eddy-current brakes exploit. The opposition principle is unchanged; only the circuit resistance limits the current.