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Michael Faraday showed in the early 1830s that moving a magnet near a wire produces a current. What he did not give was a simple way to say which way the current flows. That rule came from Heinrich Friedrich Emil Lenz in St Petersburg, and it is still the first thing you use in any induction problem. This post covers what Lenz actually wrote, why the rule must be true, and a worked example that shows the energy balance.
Who was Lenz?
Lenz was born in Dorpat (now Tartu, Estonia) in 1804 and died in Rome in 1865, according to the Deutsche Biographie index. A history page at the Hebrew University of Jerusalem records that as a young man he sailed on Otto von Kotzebue's voyage around the world in 1823 to 1826, measuring the temperature and salinity of seawater, and later joined the St Petersburg Academy of Sciences.
His published work shows a careful experimentalist. Titles in Annalen der Physik include a study of ocean water at different depths, with respect to temperature and salt content (1830), one on how the electrical conductivity of metals changes with temperature (1835), and one on the laws of heat produced by a galvanic current (1843), the heating law now often called the Joule-Lenz law.
What did Lenz actually write in 1834?
His paper, On determining the direction of galvanic currents excited by electrodynamic induction, was read to the Imperial Academy of Sciences in St Petersburg on 29 November 1833 and printed in Annalen der Physik in 1834. Its full text is on the Internet Archive. Translated from the German, his rule says:
When a metal conductor moves near a current or a magnet, a current is induced in it in such a direction that, had the wire been at rest, this current would have made it move in exactly the opposite direction to the motion actually given to it.
Notice that Lenz framed it in terms of motion and force, not magnetic flux. The version in your textbook, that the induced current opposes the change in flux, is a later restatement of the same idea. Lenz then tested the rule against a series of paired experiments, matching each known electromagnetic motion with the induction case it predicts.
Why must the induced current oppose the motion?
Suppose it did the opposite. Push a magnet towards a coil, and the coil's current attracts the magnet further in. The magnet speeds up, the current grows, the pull grows, and you have built a machine that creates kinetic and electrical energy from nothing. That breaks conservation of energy. So the only consistent direction is the opposing one, and the work you do against that opposing force becomes the electrical energy in the circuit.
A worked example: where does the energy go?
A metal rod of length L = 0.20 m slides at a steady v = 2.0 m/s along two rails, in a uniform magnetic field B = 0.50 T perpendicular to the rails. The rails are joined by a resistor, and the total resistance of the circuit is R = 0.50 Ω.
Induced emf. ε = BLv = 0.50 × 0.20 × 2.0 = 0.20 V.
Current. I = ε ÷ R = 0.20 ÷ 0.50 = 0.40 A.
Force on the rod. F = BIL = 0.50 × 0.40 × 0.20 = 0.040 N. By Lenz's rule this force points against the velocity, so you must push with 0.040 N to keep the speed steady.
Mechanical power you supply. P = Fv = 0.040 × 2.0 = 0.080 W.
Electrical power turned into heat. P = I²R = 0.40² × 0.50 = 0.16 × 0.50 = 0.080 W.
The two powers are equal. Every joule you put in by pushing comes out as heat in the resistor, which is exactly what Lenz's direction requires. If you want more practice on finding directions in coils and loops, our guide to Faraday's and Lenz's laws works through the standard cases.
What mistakes do students make with Lenz's rule?
Opposing the field instead of the change. The induced current opposes the change in flux, not the flux itself. A magnet moving away induces a current that tries to keep the flux, so it attracts.
Forgetting the force direction in rod problems. The magnetic force on the induced current always opposes the rod's velocity. If your force helps the motion, recheck your current direction.
Treating the minus sign as decoration. In ε = −dΦ/dt, the minus sign is Lenz's rule. Dropping it loses the direction.
Thinking it only applies to moving magnets. It applies to any change in flux, including a changing current in a nearby coil.
What can a student take from Lenz's way of working?
Lenz did not stop at a rule that fitted one experiment. He looked for the general principle behind many experiments and tested it against each one. Try the same with your own revision: for every induction problem, ask what the opposing force or opposing current is, and check that energy balances. For the American side of the same story, read about Joseph Henry and self-induction.
When a direction question keeps tripping you up, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning, so you can see why the current flows the way it does.
Redo the worked example with v = 4.0 m/s and check that both powers become four times larger.
