Drop a strong magnet down a copper pipe and it drifts down slowly, as if the pipe were full of honey. The reason is one short rule about the direction of induced current, and the same rule shapes motors, transformers, relays and brakes.
Lenz's law tells us which way an induced current flows: always so that its own magnetic field opposes the change that produced it. That single idea explains magnetic braking, back EMF and the minus sign in Faraday's equation.
What Is Lenzs Law?
Lenz's law states that the current induced in a closed conductor by a changing magnetic flux always flows in a direction whose own magnetic field opposes that change in flux. It does not tell you how large the voltage is, which comes from Faraday law of electromagnetic induction, but it tells you the direction every time.
Note the word change in Lenz's law. The induced current does not oppose the magnetic field itself, it opposes any increase or decrease of the flux through the loop.
The law was published by the Baltic German physicist Heinrich Lenz in 1834. The National MagLab notes that it is a consequence of the conservation of energy and that the symbol L used for inductance honours his work.
The Minus Sign in Faraday's Equation
Engineers usually write Faraday's result and Lenz's law together in one equation. The size of the EMF depends on the number of turns and the rate of change of flux, while the minus sign carries the direction rule.
Φ = B × A × cos θ
Induced current I = |EMF| ÷ R
N = turns, Φ = flux in webers, B = flux density in tesla, A = loop area in m², R = loop resistance
Example: N = 200, A = 10 cm² = 0.001 m², B falls from 0.6 T to 0.2 T in 50 ms, R = 8 Ω
ΔΦ = 0.001 × (0.2 minus 0.6) = minus 0.0004 Wb
EMF = minus 200 × (minus 0.0004) ÷ 0.05 = 1.6 V
I = 1.6 ÷ 8 = 0.2 A, its field aids the original field to resist the decrease
The positive answer in the example tells us that the induced EMF acts to keep the flux from falling. If the flux were rising instead, the sign would flip and the induced field would push against the original one.
In a coil carrying its own changing current, the same sign appears as self induced voltage, the basis of the inductor working principle. This is why current in an inductor cannot change instantly.
Why Opposition Means Energy Is Conserved
Imagine the opposite rule, where the induced current helped the change. A magnet pushed into a coil would be pulled in faster, which would induce more current and pull harder again, creating energy from nothing.
Lenz's law prevents this. Pushing a magnet towards a closed coil always meets a small repelling force, and the mechanical work you do against it is exactly the electrical energy that appears as heat in the coil resistance.
A magnet moved near an open coil feels no braking force at all. The EMF still appears across the open ends, but without current there is no opposing field and no energy is drawn.
4 Steps to Find the Induced Current Direction
For example, if the north pole of a magnet approaches a coil, the flux towards the coil rises. The near face of the coil therefore becomes a north pole to repel the magnet, and the right hand grip rule gives the current direction.
When the same magnet is pulled away, the near face becomes a south pole that tries to hold it back. The galvanometer needle swings the opposite way, exactly as Lenz's law predicts.
Lenz's Law Calculator
Second Worked Example: Magnet Approaching a Coil
A coil of 500 turns sees its flux rise from 0 to 2 mWb in 0.1 s as a magnet approaches. The EMF magnitude is 500 × 0.002 ÷ 0.1 = 10 V, and with a 50 Ω circuit the current is 0.2 A.
Because the flux is increasing, Lenz's law says the coil sets up a field pointing against the magnet field. Pull the magnet away in the same 0.1 s and the EMF is still 10 V, but the current reverses.
Magnet in a Copper Pipe: Measured Results
Levin, da Silveira and Rizzato of the Federal University of Rio Grande do Sul dropped 6 g neodymium magnets through a copper pipe 1.7 m long. One magnet took 22.9 s to fall, while a non magnetic object covered the same pipe in less than a second.
Their braking model shows that the terminal speed is proportional to the resistivity of the pipe and inversely proportional to its wall thickness. A better conductor or a thicker wall carries larger eddy currents, so the braking force is stronger.
The University of Colorado physics lab reports a similar result for a 61 cm tube, where the magnet takes about 10 s while pennies fall through in under a second. IOP Spark suggests treating the pipe as a stack of one turn coils, each obeying Lenz's law.
The copper pipe is not magnetic, so it never attracts the magnet when nothing moves. The braking force appears only while the magnet falls and vanishes the moment it stops.
Where Lenz Opposition Shows Up
Loops of current induced inside solid metal that oppose the flux change.
Voltage generated in a rotating motor that opposes the supply voltage.
Voltage across a coil that opposes a change in its own current.
Eddy currents waste energy in transformer cores, which is why cores are laminated, as explained in eddy current loss and hysteresis loss. The same opposing currents push alternating current towards the conductor surface, described in skin effect in conductors.
In a motor, back EMF rises with speed and limits the current drawn from the supply. Our article on back EMF in motors and generators shows why a stalled motor draws such a large current.
7 Powerful Lenz's Law Examples
An induction motor rotor follows the rotating field because its induced currents try to cancel the relative motion, which is why it always runs with some slip. The full story is in how an AC induction motor works and induction motor slip.
Relay and contactor coils produce a large reverse voltage when switched off, because the collapsing flux tries to keep the current flowing. This is why relay coil suppression uses a diode or an RC snubber to protect the switching device.
Apex Magnetics points out that eddy current brakes, a direct use of this induction rule, keep working even if power is lost, because they need no electricity. That makes them attractive for amusement rides and high speed trains.
When a relay driver transistor keeps failing, check the coil suppression diode first. A missing or reversed diode lets the Lenz kickback voltage reach the transistor at every switch off.
How Lenz's Law Works in a Transformer
This chain explains why primary current rises automatically when you load the secondary. Turns set the voltage ratio, as covered in transformer turns ratio, while the opposing secondary flux sets the current balance.
A current transformer relies on the same opposing flux to keep its core flux small. That is why opening a loaded CT secondary is dangerous, because the opposing flux suddenly disappears.
Faraday's Law and Lenz's Law Compared
| Point | Faraday's law | Lenz's law |
|---|---|---|
| Tells you | Size of the induced EMF | Direction of the induced current |
| Key quantity | Rate of change of flux | Sign of the flux change |
| In the equation | N × dΦ ÷ dt | The minus sign |
| Rests on | Experimental induction results | Conservation of energy |
Both laws work together in every induction sensor, from an electromagnetic flow meter to an inductive proximity sensor. The flow meter uses the size of the EMF, while the proximity sensor detects the energy taken by eddy currents in the target.
- Contactless braking with no wear.
- Self limiting current in motors.
- Predictable current direction in design.
- Induction heating without flames.
- Eddy current losses in cores and frames.
- Voltage spikes when coils are switched off.
- Inrush and kickback stress on switches.
- Heating of nearby metal parts.
Lab Demonstration Checklist
- Use a strong neodymium magnet that slides freely in the pipe.
- Choose a thick walled copper or aluminium pipe.
- Drop a non magnetic object of similar size as a control.
- Time several drops and take the average.
- Place a soft cushion below the pipe to catch the magnet.
- Keep magnets away from phones, cards and pacemakers.
Try the pipe demonstration with a slotted pipe as well. The slot breaks the circular eddy current path, so the magnet falls much faster, which proves the currents really flow around the pipe.
Electromagnetic Braking Paper PDF
Copper Tube Demonstration Video
Lenz's Law FAQ
It states that an induced current always flows so that its magnetic field opposes the change in flux that produced it. The law gives direction, while Faraday's equation gives magnitude.
The opposition is to the change and not to the field itself. When flux falls, the induced field actually points the same way as the original field.
The minus sign is how Lenz's law is written in mathematical form. It shows that the induced EMF always works against the change in flux linkage.
Without it, the equation would predict energy appearing from nothing in every coil. Most textbooks therefore say the sign represents the direction rule named after Heinrich Lenz in 1834.
A magnet pushed into a closed coil meets a repelling force from the induced current. You must do mechanical work with your hand to overcome that force.
That work turns into electrical energy and finally heat in the coil resistance. If the current helped the motion instead, energy would be created freely, which never happens in nature.
The moving magnet changes the flux through each ring of the pipe and induces circular eddy currents. Those currents create fields that oppose the motion of the magnet.
Levin and colleagues measured a fall time of 22.9 seconds through a 1.7 metre pipe. A non magnetic object of similar size fell through in under one second.
Back EMF is the voltage generated in the rotating armature or stator windings of a running motor. It opposes the supply voltage that drives the current.
As speed rises the back EMF rises too, so the current falls to the level needed for the load. A stalled motor has no back EMF and draws a very large current.
When the coil current is switched off, the collapsing flux induces a voltage that tries to keep the current flowing. This spike, predicted by Lenz's law, can be many times the supply voltage.
A diode across the coil gives the current a safe path to decay slowly. It protects the transistor or contact that switches the coil off.
It explains eddy current brakes, induction heating, induction motors and transformer current balance. It also explains why transformer and motor cores are laminated to cut eddy losses.
Sensors such as inductive proximity switches and flow meters rely on the same induction rules. Engineers meet the law whenever a coil, a magnet or moving metal is involved.
Related Articles
- Faraday's Law of Electromagnetic Induction
- Eddy Current Loss and Hysteresis Loss
- AC Motors and Generators Back EMF
- Inductor Working Principle
- Skin Effect in Conductors
External References
- Electromagnetic Braking: A Simple Quantitative Model, Levin, da Silveira and Rizzato
- Electromagnetic Braking in a Copper Pipe, IOP Spark
- Lenz's Law, Wikipedia
What We Learn Today
- Lenz's law says the induced current always opposes the change in magnetic flux that caused it, which is why Faraday's equation carries a minus sign.
- The opposition is a direct result of energy conservation, because the work done against the opposing force reappears as heat in the conductor.
- Eddy current brakes, motor back EMF, relay coil kickback and transformer current balance are everyday engineering examples of the same induction rule.