Why Does a Magnet Fall Slowly Through a Copper Pipe? Lenz’s Law

Drop a strong neodymium magnet down a copper pipe and it does something that looks wrong. It doesn’t clatter through in a fraction of a second. It drifts, as if the pipe were full of honey, and emerges at the bottom long after a plain steel ball would have. Copper is not attracted to a magnet the way iron is, so there is no sticking. What is happening is one of the cleanest demonstrations of electromagnetic induction there is, and it has a name: Lenz’s law. It is the rule our sticker Lenzor was built to embody.

What is Lenz’s law?

In 1831 Michael Faraday showed that a changing magnetic field through a loop of wire drives a current in that loop (Britannica, Faraday’s law^[1]). Faraday’s own account of those experiments was published in his Experimental Researches in Electricity (Faraday^[2]). Three years later the Russian physicist Heinrich Lenz worked out which way that current flows (Lenz 1834^[3]). His answer, in modern words: the induced current always flows in the direction that opposes the change in magnetic flux that produced it (Britannica, Lenz’s law^[4]).

In the equation for Faraday’s law, Lenz’s law is the minus sign:

ℰ = −dΦ_B/dt

Here ℰ is the induced electromotive force around a loop and Φ_B is the magnetic flux through it. The size of the effect comes from how fast the flux changes; the sign tells you the response always pushes back.

Why does a magnet fall slowly through a copper pipe?

The pipe is a stack of loops

Think of the pipe as an endless stack of copper rings. As the magnet falls, the flux through the rings just below it is increasing, and the flux through the rings just above it is decreasing. Each ring responds with a circulating current (an eddy current) that fights its own change:

• Rings below the magnet make a field that repels the approaching magnet.
• Rings above the magnet make a field that attracts the departing magnet.

Both effects point the same way: upward on the magnet. The pipe is not attracting the magnet; it is resisting its motion.

Faster means more braking, so it hits a terminal speed

The faster the magnet falls, the faster the flux changes, the bigger the induced currents and the bigger the retarding force. So the braking force grows with speed. Very quickly the upward magnetic drag equals the magnet’s weight, the net force is zero, and the magnet falls at a steady terminal velocity. MacLatchy, Backman and Bogan turned this classroom demo into a quantitative experiment, calculating and measuring the terminal velocity and the magnetic forces for a button magnet in copper and aluminium tubes (MacLatchy, Backman & Bogan 1993^[5]).

What sets how slow it goes?

In a simple model the drag force is proportional to the speed, F ≈ kv, so the terminal speed is v_t ≈ mg/k. The constant k grows with the electrical conductivity of the pipe, the strength of the magnet and how close the magnet sits to the wall, and it depends on the wall thickness. That is why a strong magnet in a thick copper pipe crawls, a weak magnet barely slows, and an aluminium pipe (lower conductivity than copper) brakes less. Cut a slot down the length of the pipe and the circulating currents can no longer flow all the way round, so the braking drops sharply.

Where does the energy go?

A magnet falling freely turns gravitational potential energy into kinetic energy. At terminal velocity its kinetic energy is constant, so where does the lost potential energy go? Into the pipe. The eddy currents flow through copper with a small but real resistance, and that dissipates energy as heat (Joule heating). The pipe warms very slightly.

This is also why Lenz’s law has to have the sign it does. If the induced currents helped the change instead of opposing it, the magnet would speed up, which would make bigger currents, which would speed it up more, creating energy from nothing. Britannica puts Lenz’s law down to conservation of energy for exactly this reason (Britannica^[4]).

Is this the same physics as magnetic brakes?

Yes. Eddy-current braking uses the same principle: move a conductor through a magnetic field (or a magnet past a conductor) and the induced currents produce a drag force that grows with speed, without anything touching. Induction cooktops and metal detectors use related induced currents too. The copper pipe is simply the most visible, hands-on version.

How does this connect to the rest of electromagnetism?

Lenz’s law is one corner of a much bigger structure. Faraday’s induction, together with the laws of electric charge, magnetic fields and currents, was unified by James Clerk Maxwell into the equations that also describe light (Maxwell 1865^[6]). Our explainer How Are Electricity and Magnetism Connected? tells that whole story, from Ørsted’s compass needle to electromagnetic waves. And if you want to know who actually got credit for what in that history, see Who Really Discovered It?

Try it (safely)

You need a strong neodymium magnet and a copper or aluminium pipe a little wider than the magnet. Drop a non-magnetic object of similar size first for comparison, then the magnet. Strong magnets can pinch fingers and can damage electronics and cards, so handle them carefully and keep them away from small children.

Wear the induction

Lenzor also appears on the Field Work sticker sheet, and the man who started it is on the Michael Faraday sticker. Browse the whole Electromagnetism collection.

FAQ

Is copper magnetic?

Not in the everyday sense: a magnet won’t stick to it. The slowing comes from induced currents, not from attraction.

Why does the magnet fall at a constant speed?

The magnetic drag grows with speed. Once it equals the magnet’s weight the forces balance, and it falls at a steady terminal velocity.

What is the minus sign in Faraday’s law?

It is Lenz’s law: the induced emf drives a current that opposes the change in flux that caused it.

Does a plastic pipe slow the magnet?

No. Plastic does not conduct, so no eddy currents flow and the magnet falls freely, apart from air resistance and friction.

References

1. Encyclopaedia Britannica — Faraday’s law of induction (Faraday’s observations of 1831). https://www.britannica.com/science/Faradays-law-of-induction
2. M. Faraday, Experimental Researches in Electricity, Vol. 1 (Project Gutenberg). https://www.gutenberg.org/ebooks/14986
3. Lenz (1834) Ueber die Bestimmung der Richtung der durch elektrodynamische Vertheilung erregten galvanischen Ströme, Ann. Phys. 107, 483–494. https://doi.org/10.1002/andp.18341073103
4. Encyclopaedia Britannica — Lenz’s law (deduced in 1834 by the Russian physicist H. F. E. Lenz; conservation of energy). https://www.britannica.com/science/Lenzs-law
5. MacLatchy, Backman & Bogan (1993) A quantitative magnetic braking experiment, Am. J. Phys. 61, 1096. https://doi.org/10.1119/1.17356
6. J. C. Maxwell (1865), “A Dynamical Theory of the Electromagnetic Field,” Phil. Trans. R. Soc. 155, 459. https://doi.org/10.1098/rstl.1865.0008

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.