Lenz's Law

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What is Lenz’s Law?

Lenz’s Law says that an induced current, a current set up by a changing magnetic field, flows so that the field it makes opposes the change that created it.

When a metallic conductor moves in the vicinity of a galvanic current or magnet, a galvanic current will be produced in it that has the direction that it would have if a motion were produced in the wire when it was at rest that would precisely oppose the one that was given to the wire, assuming that when the wire was at rest, it could move only in the direction of motion and the opposite direction.

That sentence is D. H. Delphenich’s English of Lenz’s 1834 paper. A galvanic current, in that paper, is the current from a battery circuit, the current we now simply call an electric current in a wire. Magnetic flux is the amount of magnetic field passing through a loop. Later textbooks compress the same direction into flux. If the flux through the loop is increasing, the induced field points against the applied field. If the flux is decreasing, the induced field points with the applied field, so as to slow the decrease. The minus sign written in front of the rate of change of flux is that direction. Lenz’s 1834 sentence does not contain the word flux, and this page does not pretend that it does. The opposition is easy to picture with a bar magnet and a coil. Push the north pole in, and the near face of the coil becomes a north pole and repels the incoming magnet. Pull the magnet out, and the near face becomes a south pole and attracts it. The current has flipped. In both motions it fights the change you are making, not the magnet as an object. The work you do against that push or pull is the energy that shows up as heat in the wire. If the induced current had helped the motion, the magnet would be dragged in, or held back on the way out, and a current would appear without that work.

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Lenz’s Law in 3 Depths

• Beginner: Push a magnet into a coil and the coil pushes back. Pull it out and the coil tugs back. Drop the magnet through a copper pipe and it crawls, because currents in the copper push against the fall. Copper is not grabbing the magnet as a permanent magnet would.
• Practitioner: Before you name the current, say whether the flux is rising or falling. Rising flux: the induced field opposes the applied field. Falling flux: the induced field points with the applied field. The current is whichever way produces that induced field. In a brake or a motor, expect a stronger opposition when the motion is faster, and leave room for the moment before that opposition has grown.
• Advanced: The 1834 test asks which current would have produced the opposite motion, then takes that opposite current. Inversion Thinking is the same shape of question outside a wire. The flux sentence and the minus sign are the later short writing of this direction. Energy is why the sign cannot be flipped. First Principles Thinking is the habit of deriving the sign from that bookkeeping. A team that resists a plan is not an eddy current, and the pipe times below do not transfer to an office.

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Origin

Lenz’s Law is the direction rule E. Lenz read to the Royal Academy of Science in St. Petersburg on 29 November 1833. It was published the next year as “Ueber die Bestimmung der Richtung der durch elektrodynamische Vertheilung erregten galvanischen Ströme,” in Annalen der Physik (Leipzig) (2) 107 (1834), pages 483–494. The name on the paper is E. Lenz. Reference notices give the fuller name Heinrich Friedrich Emil Lenz and the years 1804–1865. This page does not add a birthday or a birthplace. Lenz starts from Faraday’s Experimental Researches in Electricity. He cites the 1832 printing in Poggendorff’s Annalen, number 5, sections 114 and 116, and says Faraday had given two direction rules for what Lenz takes to be one phenomenon. One rule covered a wire moving toward or away from a current. The other covered a wire moving near a magnet. Lenz also says Faraday’s own picture, a knife blade moved along a magnet, still left the direction hard to see. He says Nobili, in the 1833 Annalen, number 3, kept only the first of Faraday’s rules. Those papers were not re-read here. What this page uses is Lenz’s report of them. His own rule reduces the induction to the electromagnetic forces already known from Ampère. Ask which current, in a wire allowed to move only forward or back along the actual motion, would have produced the opposite motion. The induced current is the opposite of that current. He writes that he hopes the agreement of this law with the experiments has been confirmed sufficiently. That sentence is his judgment. It is not a table of angles. One trial he reports as his own uses two circular conductors, each of twenty windings of coated copper wire, sharing the arrangement of an Ampère rotation experiment. One conductor is connected to a zinc-copper pair two square feet in area. The other is connected to a sensitive Nobili multiplier, a many-turn galvanometer. He states that when the mobile conductor is brought from perpendicular to parallel, the induced current is opposite the current in the fixed conductor. He does not print a scale reading. A foot-long coil side, a five-inch magnet, and a mercury-float magnet in a later footnote are also in the paper. Those dimensions are not used below. Footnote 2 says Ritchie, on page 206 of the same volume, got the same law wrong, unless Lenz misunderstood him. Ritchie was not re-read, and that dispute is not a result on this page.

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Key Points

Four distinctions keep the 1834 direction, the later flux sentence, and a measured fall from being treated as one number.

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Applications

Use the direction when you can point to a changing flux and a conducting path. Do not carry the pipe’s seconds into a kitchen, a motor nameplate, or a meeting.

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Case Study

In 2006 Yan Levin, Fernando L. da Silveira, and Felipe B. Rizzato, at the Instituto de Física of the Universidade Federal do Rio Grande do Sul in Porto Alegre, wrote up a magnet falling through a copper pipe. The copy read here is arXiv physics/0603270v2, updated 6 September 2006. The journal line on that record is American Journal of Physics, volume 74, page 815 (2006), DOI 10.1119/1.2203645. The journal PDF was not re-read. The numbers below are the arXiv text. They ask a class question. A long pipe of non-ferromagnetic metal is held vertical. A small magnet is released at the top. Does it fall faster, slower, or just as fast as a non-magnetic object of the same mass and shape? Their answer is slower, and they call the crawl a demonstration of Faraday’s law and Lenz’s Law. The pipe is copper, length 1.7 m, radius 7.85 mm, wall thickness 1.9 mm. They use three neodymium cylinders, each of mass 6 g, radius 6.35 mm, and height 6.35 mm, plus a stopwatch and a teslameter. One magnet takes 22.9 seconds to pass through the pipe. Two magnets stuck together take 26.7 seconds. Three take 23.7 seconds. They write that a non-magnetic object covers the same distance in less than a second. They do not print that object’s time, and this page does not invent one. They also write that terminal speed is reached very quickly, so a constant speed, length divided by time, is fair for the whole pipe. In units of 10⁻² m/s, the measured speeds are 7.4, 6.4, and 7.2. Dividing 1.7 m by 22.9 s, 26.7 s, and 23.7 s gives those three figures once they are rounded as the table rounds them. The face field, measured with the teslameter probe against the center of a flat face, is 393, 501, and 516 millitesla for one, two, and three magnets. Their calculated speeds, in the same hundredths of a meter per second, are 7.3, 5.8, and 6.9. The two-magnet row is the wide one: 6.4 measured against 5.8 calculated. They still say the simple theory accounts quite well for the findings, and that it correctly puts the two-magnet stack slower than either one magnet or three. A point-dipole approximation would have doubled the time when a second magnet was added. In that approximation the time scales with the square of the dipole and inversely with the mass, and both the dipole and the mass double. The measured time went from 22.9 seconds to 26.7 seconds, which is not a doubling. They treat that miss as a reason to drop the point dipole for a magnet whose length is comparable to the pipe’s radius. The energy sentence is theirs. At constant speed the kinetic energy is steady, so the lost gravitational energy has to become something else. They say that something else is ohmic heating in the copper, and they set the weight times the speed equal to the sum of current-squared times resistance. Lenz’s Law supplies the direction of those currents: each ring of pipe repels an approaching magnet and attracts a receding one, and the net force is a drag. Faraday’s law supplies the size of the induced voltage from the rate of change of flux. The 22.9 seconds are what this pipe, these magnets, and this stopwatch produced. They are not a law of falling objects.

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Boundaries and Failure Modes

Lenz’s Law is the wrong summary in three uses. One asks the direction rule to produce 22.9 seconds. Another gives a different pipe this pipe’s time. A third describes a person who resists a change as an induced current. The first boundary is the apparatus and the model that sits on it. The times 22.9, 26.7, and 23.7 seconds belong to one setup. So do the speeds 7.4, 6.4, and 7.2, in units of 10⁻² m/s. The copper pipe is 1.7 m long, with radius 7.85 mm and wall 1.9 mm. The neodymium cylinders are 6 g each, with radius 6.35 mm and height 6.35 mm, stacked one, two, or three deep. The calculated column is not the 1834 law. It replaces each magnet with two point magnetic charges, it extends the heating integral to an infinite pipe because most of the loss is near the magnet, and the authors set self-induction aside. They say the magnet’s motion is slow beside the decay of the eddy currents, and they cite Smythe’s 1950 book and Saslow’s 1992 paper for that separation. Those two works were not re-read. The two-magnet gap, 6.4 against 5.8, stays visible. “Quite well” is their phrase. It does not erase the gap. The second boundary is a different conductor. A slit changes the paths the eddy currents can take. Keith Zengel and coauthors report a slit pipe in American Journal of Physics, volume 93, number 3, March 2025, pages 223–233, DOI 10.1119/5.0216717. The abstract says the drag is smaller than in an intact pipe of the same radius. It also says slits reduce, but do not eliminate, the horizontal currents that produce the vertical drag. The PDF was not re-read. This page prints no speed, no slit width, and no magnet count from that paper. An open single-turn ring is a stronger break: there is no closed loop for the current Lenz’s coils were built to carry. Do not describe every cut as “no effect,” and do not describe every intact pipe as 22.9 seconds. The third boundary is the misuse. Newton’s Third Law says that when one body pushes a second, the second pushes the first with an equal force the other way. The two forces act on two bodies. Lenz’s Law chooses the direction of a current. The likeness is the word oppose. It is not an identity, and this page does not borrow a rocket, a walk, or a recoil from that page. Systems Thinking can call a restoring response negative feedback. An organization, a habit, or a child pushing back is not the copper pipe. The heating ledger does not apply to them, and neither does 7.4 × 10⁻² m/s.

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Common Misconceptions

Three retellings turn a direction into a repulsion that never flips, a stopwatch reading into the law, or a slow fall into a magnetic metal.

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Related Concepts

The direction rule sits next to five neighbors. One is a force pair that is not the same law. The others are a reversed question, a ledger that fixes a sign, a restoring loop, and a second effect that acts back on the first.

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One-Line Takeaway