Lenz’s law states that when a changing magnetic field induces an electric current in a conductor, that current flows in a direction that opposes the change that created it. In simpler terms, nature resists changes in magnetic fields by generating currents that push back. First formulated in 1834 by Russian physicist Heinrich Lenz, this principle explains why magnets slow down when dropped through copper tubes, why electric motors don’t spin infinitely fast, and why electromagnetic brakes work on roller coasters.
The Core Idea in Plain Language
Imagine pushing a magnet toward a coil of wire. As the magnet gets closer, the magnetic field passing through the coil increases. That changing field generates a voltage (called an electromotive force, or emf) in the wire, which drives a current. Lenz’s law tells you which way that current flows: it will always create its own magnetic field that pushes back against the approaching magnet. If you pull the magnet away instead, the current reverses direction and now tries to pull the magnet back in. The induced current always fights whatever change is happening.
This isn’t arbitrary. It’s a direct consequence of conservation of energy. If the induced current helped the magnet move closer instead of opposing it, the magnet would accelerate on its own, generating even more current and more acceleration, creating energy from nothing. That would violate one of the most fundamental rules in physics. The opposition described by Lenz’s law ensures that energy is always accounted for: you have to do work (push the magnet) to generate current, and that work is what becomes electrical energy.
Where It Fits in the Math
Lenz’s law is built into Faraday’s law of induction through a single negative sign. Faraday’s law says the induced voltage equals the negative rate of change of magnetic flux through a loop: emf = −N(ΔΦ/Δt), where N is the number of loops in a coil and Φ is the magnetic flux. The magnitude tells you how strong the induced voltage is. The negative sign is Lenz’s law, telling you the direction of that voltage opposes the flux change.
Without the negative sign, the equation would still give you the correct strength of the induced voltage, but you’d have no way to know which direction the current flows. That’s the specific job of Lenz’s law: it resolves the direction question.
How to Predict Current Direction
You can determine which way induced current flows in three steps. First, figure out whether the magnetic flux through the loop is increasing or decreasing. Second, apply Lenz’s law: the induced current will create a magnetic field that opposes that change. If flux is increasing, the induced field points opposite to the external field. If flux is decreasing, the induced field points in the same direction as the external field, trying to maintain it. Third, use the right-hand rule to find the current direction. Curl the fingers of your right hand in the direction current would flow; your thumb points in the direction of the magnetic field that current produces. Match the thumb to the opposing field direction you identified, and your curled fingers show the current’s path.
Back EMF in Electric Motors
Every electric motor contains coils of wire spinning inside a magnetic field. That spinning coil experiences a changing magnetic flux, which induces a voltage that, per Lenz’s law, opposes the input voltage powering the motor. This opposing voltage is called back emf. It’s the reason a motor draws much less current at full speed than it does the instant you turn it on. When the motor first starts, the coil isn’t spinning yet, so there’s no back emf and a large current rushes in. As the motor speeds up, back emf builds and reduces the net voltage driving the current. If you stall a motor by holding its shaft, back emf drops to zero and current spikes, which is why stalled motors overheat.
Eddy Currents and Electromagnetic Braking
When a sheet of metal moves through a magnetic field, the changing flux induces tiny swirling currents throughout the metal called eddy currents. These currents generate their own magnetic fields that, following Lenz’s law, oppose the motion of the metal. The result is a braking force that slows the metal down without any physical contact.
This effect is used in braking systems on trains and roller coasters. As a metal plate enters a magnetic field, increasing flux creates eddy currents that push the plate backward. When the plate exits the field, decreasing flux creates eddy currents that again resist the motion. The braking force is proportional to speed, so it’s strongest when the vehicle is moving fast and drops to zero when the vehicle stops. That makes electromagnetic brakes inherently smooth, and because there’s no friction involved, rain and weather don’t affect their performance. The tradeoff is that eddy current brakes can’t bring something to a complete stop on their own. They might reduce speed from 20 m/s to 5 m/s, but a conventional brake is still needed for the final stop.
This also explains the classic physics demonstration where a magnet falls slowly through a copper or aluminum tube. The falling magnet induces eddy currents in the tube walls, and those currents create fields that oppose the magnet’s descent. The magnet still falls, but dramatically slower than it would through a non-conductive tube like glass. The material doesn’t need to be magnetic itself. It just needs to conduct electricity. Copper and aluminum work well because they’re excellent conductors.
Magnetic Levitation in Trains
Some maglev trains use Lenz’s law as their levitation mechanism. In electrodynamic suspension systems, superconducting magnets on the train pass by figure-eight-shaped coils mounted along the guideway. As the train moves at high speed, the magnets induce currents in these coils. Because the magnets pass below the center of the figure-eight shape, the lower half of each coil experiences a greater change in flux than the upper half. This asymmetry produces a net upward magnetic force that lifts the train off the track. The faster the train moves, the stronger the induced currents and the greater the levitation force, which is why these systems only achieve full levitation above a certain speed.
Why It Works With Any Conductor
Lenz’s law applies to any material that conducts electricity, not just magnetic metals like iron or steel. Copper, aluminum, silver, and gold all experience induced currents when exposed to changing magnetic fields. The strength of the effect depends on how well the material conducts. A highly conductive material like copper produces stronger eddy currents and a more pronounced opposing force. A poor conductor like stainless steel produces weaker effects. A non-conductor like glass or plastic produces no induced current at all, because there are no free electrons to move. This is why the material of the cookware matters on an induction stovetop, and why dropping a magnet through a glass tube looks nothing like dropping one through a copper tube.