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Break a circuit with a long coil of wire in it and you may see a spark jump at the switch. Joseph Henry noticed this in 1832 and recorded it carefully enough that we now credit him with discovering self-induction. This post covers his life, what his 1832 paper says, and how to work out why the spark appears.
Who was Joseph Henry?
The Smithsonian Institution Archives says Henry was born in 1797 in Albany, New York, and was too poor to attend the Albany Academy until he was about 21. In 1826 he became the Academy's professor of mathematics and natural philosophy, and began research on electromagnetism there. In 1832 he moved to the College of New Jersey, now Princeton University. On 3 December 1846 he became the first Secretary of the Smithsonian Institution, and he served until his death on 13 May 1878.
The Princeton Companion entry on Henry adds that he was the first to wind insulated wire around an iron core to make powerful electromagnets, built one for Yale that lifted 2,300 pounds, and that the unit of inductance, "the henry", is named after him.
What did Henry report in 1832?
His paper On the Production of Currents and Sparks of Electricity from Magnetism appeared in the American Journal of Science in July 1832 (volume 22, pages 403 to 408). He explained that he had started building a large electromagnet the previous August to look for electricity from magnetism, was interrupted, and meanwhile read a short report that Faraday had succeeded.
He then described his own method, which he said differed from Faraday's. About thirty feet of insulated copper wire was coiled around the iron armature of his electromagnet, which could hold six to seven hundred pounds. When the battery was switched on, a distant galvanometer needle jumped one way; when it was switched off, the needle jumped the other way; in between, nothing. He concluded that a current is produced "for an instant" whenever magnetism appears in the iron, and in the opposite direction when it disappears.
How did a spark reveal self-induction?
The important observation comes near the end, almost as an aside. Henry wrote that with a short copper wire, "not more than a foot in length," across a small battery, no spark appears when the circuit is made or broken. But with a wire "thirty or forty feet long," breaking the connection gives "a vivid spark." The effect grew when the wire was coiled into a helix.
His explanation: "the long wire" becomes "charged with electricity which by its reaction on itself projects a spark when the connection is broken." In modern words, the changing current in the wire changes the magnetic field around the wire itself, and that change induces an emf in the same wire. That is self-induction.
Why does breaking the circuit make a spark? A worked example
A coil's self-inductance L links the emf it produces to how fast its current changes: ε = L × (ΔI ÷ Δt). Here is why breaking a circuit is so different from making it.
Take a coil with L = 0.50 H carrying I = 2.0 A from a battery of a few volts.
Breaking quickly. Suppose the current falls to zero in 0.010 s. ΔI ÷ Δt = 2.0 ÷ 0.010 = 200 A/s. ε = 0.50 × 200 = 100 V.
Breaking faster. If the switch opens in 0.0010 s, ΔI ÷ Δt = 2000 A/s and ε = 0.50 × 2000 = 1000 V.
Energy available. The coil stores U = ½LI² = 0.5 × 0.50 × 2.0² = 1.0 J. That energy has to go somewhere when the current stops, and a spark across the gap is one way out.
When the circuit is made, the current rises gradually and the induced emf only opposes the battery's few volts, so there is no spark. When it is broken, the current must collapse almost instantly, and the emf can be far larger than the battery voltage. This also explains Henry's long-wire result: a longer wire, especially coiled, has more inductance.
What mistakes do students make with self-induction?
Thinking the induced emf helps the change. By Lenz's rule it opposes it. When current falls, the self-induced emf tries to keep it flowing, which is why the spark jumps.
Mixing up L and ΔI ÷ Δt. A small inductance can still give a large emf if the current changes fast enough.
Forgetting the energy. ½LI² is energy stored in the magnetic field. It does not vanish when you open a switch.
Our guide to self and mutual inductance covers the formulas you need for JEE and boards, and our post on Heinrich Lenz explains the direction rule.
What can a student take from Henry's way of working?
Henry was largely self-educated, built much of his own apparatus, and was candid in print that Faraday and James Forbes had published related results first. What stands out is how exactly he recorded each condition: the length of wire, the cups of mercury, the direction of each needle swing. That precision is what made a passing remark into a discovery.
If you want to watch how a changing current in a coil produces an opposing emf, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Rework the example for L = 0.20 H and I = 3.0 A, breaking in 0.005 s, and check the stored energy too.
