Eddy Currents

Drop a strong neodymium magnet down a half-metre copper pipe and something looks broken. A steel bolt clatters through in a third of a second; the magnet takes about eleven seconds, gliding down in eerie slow motion, touching nothing. Copper is not magnetic — check it with the classification drill from Classify the Material — χ, μᵣ & Behaviour and you find a feeble diamagnet, a million times too weak to matter. What grips the magnet is something the magnet itself creates: whirlpools of current, conjured in the pipe wall by its own falling flux, each one obeying Lenz's Law & Energy Conservation and pushing back against the fall. These whirlpools are eddy currents — Foucault currents, after the man who caught them heating a copper disc in 1855. They are what happens when induction meets solid metal. Faraday's Law of Induction was stated for tidy circuits: one loop, one path, one current. But a solid plate is a circuit everywhere — a changing flux can drive current around any closed path inside it, and the metal improvises thousands of them at once, like river water swirling behind a rock. No terminals, no wires, yet real amperes, real heat, real forces. This module is the chapter's applications engine: magnetic brakes on trains and drop towers, the dead-beat damping that stills a galvanometer needle, the induction cooktop in your kitchen, and the laminated cores that keep transformers from cooking themselves. It is also an honesty checkpoint: CBSE quietly dropped eddy currents in its 2023 rationalization, while JEE-Main, NEET and ISC still name them explicitly — the traps section sorts out exactly who examines what.

Key takeaways

A changing magnetic flux through bulk metal drives closed loops of current — eddy currents — swirling inside the material with no wires needed; direction always by Lenz: oppose the change.
Because a chunk of metal has tiny resistance, even a modest induced emf drives large currents: violent heating and strong forces come standard.
Moving-conductor eddies produce a drag that grows with speed and dies at rest — friction without contact, the physics of train brakes, drop towers and dead-beat meters.
The same currents are a menace inside transformer and motor cores; the fix is lamination — slicing the core into insulated sheets that cut the eddy loops but not the useful flux.
Friend or foe is a design choice: induction furnaces and cooktops want the heat; core designers kill it; brake designers want the force.
Key idea: eddy currents are induced currents set loose in solid metal — Lenz-obedient whirlpools whose drag and heat you either harvest or engineer away.

The core insight

Eddy currents are loops of induced current circulating inside bulk conductors wherever magnetic flux changes; they obey Lenz's law — opposing the change that made them — which makes them simultaneously nature's cleanest brake, an unavoidable heat leak in machine cores, and a heater you can switch on through solid metal.

Where this lives today

Eddy currents earn their keep as sensors. Aircraft maintenance crews sweep a small AC coil over wing skins and turbine discs: surface cracks interrupt the local eddy loops, the coil feels the change, and flaws a hair's width across are mapped without touching or dismantling anything — the aviation industry's standard crack hunter. Airport metal-detector arches and coin validators read the same signature: pulse a field, listen to the eddies' decay, and the machine knows metal from plastic and one alloy from another in milliseconds. In the kitchen, an induction cooktop drives twenty-something-kilohertz flux into the pan base; the eddies heat the metal directly while the glass stays cool, and the pan must be ferromagnetic-ish for the heating to work well — your cookware shopping is applied Classify the Material — χ, μᵣ & Behaviour. On the high-speed rail lines of Europe and Japan, eddy-current brakes press nothing against nothing: electromagnets hover over the rail, drag scales with speed, and the friction pads are saved for the final walking-pace stop. Amusement-park drop towers use the same trick in its fail-safe form — copper fins on the car passing permanent magnets on the tower brake the fall with no power, no computer, no wear. And inside every substation transformer hums the negative image of all this: thousands of varnished steel sheets, stacked precisely so that the currents this module celebrates never get to flow. That story — and the $n^2$ payoff of thinner sheets — is cashed in The Transformer, two chapters ahead.

The physical picture

Slide a solid copper plate between the poles of a strong magnet. Focus on any imaginary loop drawn inside the metal — a circle the size of a coin, say. As the plate moves, the flux through that circle changes, and Faraday's Law of Induction insists an emf appears around it. In a wire circuit, that emf would drive current around the one path available. In a plate, every such circle is a path: the metal conducts in all directions, so currents bloom wherever the flux is changing, swirling in closed whirlpools — strongest near the pole edges, where a moving patch of metal sees its flux rise or fall most steeply. Each whirlpool has a direction, and Lenz's Law & Energy Conservation dictates it without exception: oppose the change. On the plate's leading edge, where metal is entering the field, flux through each little loop is rising — so the eddies circulate to push back, making that patch of plate behave like a magnet face-to-face with its own reflection. On the trailing edge, flux is dying, and the eddies there circulate the other way, clinging to the field like a magnet being pulled apart from its partner. Repelled at the front, held back at the rear — every whirlpool votes the same way: against the motion. The sum is a smooth drag force that grows with speed and vanishes at rest.

Figure

Eddy whirlpools in a moving plate — leading edge repelled, trailing edge held back, every loop voting against the motion

Why are the effects so violent in solid metal, when the same flux change in a thin wire loop drives a mild current? Resistance. An induced emf of a fraction of a volt is nothing special — but drive it around a fat, short path through a copper block whose resistance is a few ten-thousandths of an ohm, and Ohm's law delivers currents of tens or hundreds of amperes. Big currents in a magnetic field mean big forces; big currents through even tiny resistance mean serious heating ( $P = \varepsilon^2/R$ with minuscule $R$ ). That single observation — solid metal is a near-short-circuit — is why eddy effects can slow a falling magnet to a crawl and melt a crucible of titanium.

The rules eddy currents obey

Everything quantitative you need is inherited, and citing the right owner earns method marks. Each imagined loop inside the metal obeys the master law from Faraday's Law of Induction:

\varepsilon = \frac{\Delta\Phi}{\Delta t} \qquad (1)

where: $\Phi = BA\cos\theta$ is the flux through that loop (the grammar of Magnetic Flux), and the emf drives a current $I = \varepsilon/R_{\text{loop}}$ around it. Read it physically: the faster the flux changes — quicker motion, stronger magnet, higher AC frequency — the bigger every whirlpool. That is why eddy drag grows with speed, and why the effects that are quaint at 50 Hz become industrial at 20 kHz. Direction never needs a new rule: run the four-step algorithm from Lenz's Law & Energy Conservation on any loop (flux direction → growing or dying → induced-field direction → curl the right hand). And the force on each whirlpool is the standard $F = BIL$ story of Force on a Current-Carrying Conductor, summed over the swirl. Eddy currents are not new physics — they are the whole chapter running loose in three dimensions. The energy ledger closes the same way it always does. Drag force times distance equals heat in the metal: a braked train's kinetic energy reappears as warmth in the rail-mounted brake discs; the slowly falling magnet's lost gravitational energy warms the copper pipe by a measurable whisker. Lenz guarantees the sign — induced effects consume mechanical energy, never amplify it — because the alternative would be a free-energy machine.

Derivation AWhy the magnet falls slowly — the copper pipe as a stack of Lenz loops

The goal is the signature demonstration, explained to marks-scheme standard: why a magnet falls through a copper pipe at a small, steady terminal speed, touching nothing. The strategy is to model the pipe as a stack of thin conducting rings and interrogate the two rings nearest the magnet with Lenz's algorithm, then let the force-versus-speed structure deliver terminal velocity. Watch how every step is inherited machinery — flux, Lenz, force on currents — assembled rather than invented; that assembly is the exam answer.

Step 1. Model the pipe. A copper pipe is electrically a stack of independent closed rings. As the magnet (say, north pole downward) falls, the ring just below it sees magnetic flux rapidly increasing; the ring just above sees its flux rapidly decreasing.

Step 2. Apply Lenz ring by ring. The ring below, fighting a flux increase, runs its current so its upper face is a north pole — north facing the falling north: repulsion, pushing the magnet up. The ring above, mourning a flux decrease, runs its current the other way, making its lower face a south pole — attracting the departed magnet, pulling it up. Both nearest neighbours, and every ring beyond them, brake the fall. Why the votes are unanimous: Lenz's law is an energy statement, not a geometric accident. Any ring that accelerated the magnet would be feeding kinetic energy from nowhere; opposition is compulsory in every ring, whichever pole falls first — flip the magnet and every current reverses, but every force still points up.

Step 3. See the speed dependence. Each ring's emf follows equation (1): proportional to how fast its flux changes, hence proportional to the magnet's speed $v$ . The ring currents are proportional to the emf, and the braking force is proportional to the currents — so the total drag has the structure $F_{\text{drag}} \propto v$ : gentle at low speed, fierce at high speed, zero at rest.

Step 4. Find the terminal state. Falling from rest, the magnet accelerates while $mg$ exceeds the drag; the drag grows with $v$ until the two balance, and from then on the descent is steady. A strong NdFeB magnet in a snug copper pipe crawls at a few centimetres per second — about 11 seconds for a half-metre pipe, versus 0.32 s for a free fall from rest over the same drop. Thicker pipe walls, a stronger magnet or a snugger fit all deepen the drag and slow the crawl; slit the pipe lengthwise and the ring currents cannot circulate — the magnet drops nearly free, the cleanest proof that circulating currents were the grip. Verified: free-fall time from rest over 0.50 m is $\sqrt{2 \times 0.50/9.8} = 0.32$ s; at a measured terminal crawl of 4.5 cm/s the same drop takes $0.50/0.045 \approx 11$ s — both recomputed. The force structure (emf ∝ v → current ∝ v → force ∝ v) mirrors the rod-on-rails drag chain of Motional EMF, where the same logic is worked with formulas.

Figure

The magnet in the copper pipe — every ring is a Lenz loop, and all of them vote to brake the fall

Friend and foe — the applications census

Eddy currents are rare among exam topics: the same physics is deliberately strengthened in one device and exterminated in the next, and questions love asking which is which.

device	eddy role	the design move
train and roller-coaster brakes	friend — drag ∝ v	electromagnets near a rail or fin; braking force strong at speed, fading gently to zero — no lurch, no wear
free-fall drop towers	friend	copper fins enter a magnet array; the ride brakes itself even in a power cut
dead-beat galvanometers	friend — damping	the coil is wound on a metal former whose eddies kill oscillation; the needle settles at once (the damping hook noted in The Moving-Coil Galvanometer)
induction furnace	friend — heating	high-frequency coil induces violent eddies in the metal charge; the metal melts in its own currents, crucible untouched
induction cooktop	friend — heating	kHz-frequency eddies heat the pan bottom directly; works best on ferromagnetic pans — the classification logic of Classify the Material — χ, μᵣ & Behaviour decides your cookware
electricity meters (old disc type)	friend — braking	a spinning aluminium disc is damped by a permanent magnet so its speed tracks power honestly
transformer cores	foe — heat loss	the AC flux that must thread the iron also stirs eddies in it; unchecked, a solid core would run scalding hot
motor and generator armatures	foe	same disease: solid iron in a changing flux is a heater you did not order

The foe rows share one cure: lamination. Slice the core into thin sheets, insulate them from each other with varnish, and stack — with the sheets parallel to the flux so the magnetic path is untouched, but the would-be eddy loops, which circulate in planes perpendicular to the flux, are chopped into segments too thin to swirl. Each thin sheet hosts only a tiny loop with a tiny emf and a long thin path of high resistance; the loss collapses (as an engineering rule, cutting sheet thickness by a factor $n$ cuts eddy loss by about $n^2$ ). Every transformer hum you have ever heard comes from a stack of such laminations — the full design story is cashed in The Transformer, in the AC chapter ahead. The precision numericals of charge-through-a-galvanometer and ramped fields, meanwhile, belong to Flux-Change Numericals — Pulls, Flips & Ramps, later in this chapter's gym.

Limiting cases

case	result	meaning
conductor at rest, steady field	no eddies	no flux change anywhere — the quiet baseline
slow motion / weak magnet	feeble drag ∝ v	eddy braking fades smoothly near rest — brakes that cannot lock
fast motion / strong magnet	fierce drag	emf ∝ v and the magnet's strength enters twice (making flux, then feeling force)
slotted or slit conductor	eddies mostly killed	loops cannot close across the cuts — the slit-pipe and comb-pendulum demos
laminated core, sheets ∥ flux	flux intact, eddies chopped	the transformer designer's move
insulator in changing flux	nothing	emf exists but no mobile charges — no currents, no heat
higher resistivity alloy	weaker eddies	why cores use silicon-steel rather than pure iron

Common trapCopper is not magnetic, so a magnet cannot grip it

Half true, and the half-truth inverts the physics. A stationary magnet indeed ignores copper almost completely — copper's diamagnetic response (χ ≈ −10⁻⁵, per the ledger of Magnetisation, Intensity & Susceptibility) is a million times too feeble to feel. But a moving magnet near copper, or copper moving near a magnet, is a different experiment: the changing flux induces real circulating currents, and those currents are full-strength electromagnets while they last. The grip in the pipe demo is not copper's magnetism — it is the magnetism of the currents the falling magnet writes into the copper, currents that exist only during the change. Freeze the motion and the grip vanishes instantly; that vanishing is the tell separating eddy effects from material magnetism, and examiners test exactly this distinction.

Worked examples

Board level — why eddy heating is violent: one loop, estimated (ISC/CBSE-style, 3 marks)

A solid copper disc spins at 50 rev/s with its face perpendicular to a uniform field $B = 0.30$ T that covers part of the disc. Consider one representative eddy loop of radius $r = 0.05$ m inside the metal, for which the flux changes at the rate $\Delta\Phi/\Delta t \approx BA\omega$ . The loop's effective resistance is $1.1\times10^{-4}\ \Omega$ . Estimate the emf around the loop and the power it dissipates, and state what this implies for the disc.

Step 1. Loop area: $A = \pi r^2 = \pi (0.05)^2 = 7.9\times10^{-3}$ m². Angular rate: $\omega = 2\pi \times 50 = 314$ rad/s.

Step 2. Emf, equation (1) with the given rate: $\varepsilon \approx BA\omega = 0.30 \times 7.9\times10^{-3} \times 314 = \boxed{0.74\ \text{V}}$ . Under a volt — unremarkable so far.

Step 3. Power. Here the solid metal shows its teeth: $P = \varepsilon^2/R = (0.74)^2 / (1.1\times10^{-4}) \approx \boxed{5\ \text{kW}}$ — from one representative loop, driven by a sub-volt emf, because the path's resistance is a ten-thousandth of an ohm.

Step 4. The implication sentence (the concept mark): a modest induced emf in bulk metal drives enormous currents and kilowatt-scale heating; this is why unlaminated machine cores overheat, why induction furnaces can melt metal, and why the disc experiences a strong retarding force — the braking Foucault measured in 1855.

Competitive level — the ratio triage: pipes, magnets and slits (NEET/JEE-Main pattern, ~2 minutes)

A magnet falls through a copper pipe at terminal speed $v_0$ . Predict the new terminal speed if, separately: (a) the pipe is replaced by an identical aluminium one (copper's conductivity is about 1.7 times aluminium's); (b) the magnet is replaced by one of twice the magnetic strength; (c) the pipe is slit end-to-end.

Step 1. Build the structure once. Drag chain: emf ∝ (magnet strength $m$ ) × $v$ ; ring current ∝ emf × (conductivity σ); braking force ∝ current × $m$ . So $F_{\text{drag}} \propto \sigma m^2 v$ , and terminal velocity — where drag equals the fixed weight — obeys $v_t \propto 1/(\sigma m^2)$ .

Step 2. Part (a): aluminium's σ is smaller by the factor 1.7, so $v_t$ rises by that factor: $\boxed{v_t \approx 1.7\,v_0}$ — the magnet falls noticeably faster, the classic lab check that conductivity, not "magnetism of the pipe", sets the grip.

Step 3. Part (b): the magnet's strength enters twice — once to make each ring's emf, once more to feel the rings' force. Doubling $m$ quadruples the drag at any speed, so terminal velocity falls fourfold: $\boxed{v_t = v_0/4}$ .

Step 4. Part (c): a lengthwise slit interrupts every ring path; circulating currents die, drag collapses, and the magnet falls essentially freely: $\boxed{v_t \to \text{(nearly free fall)}}$ . One cut kills the effect — the same reason laminating a core works. Timing note: two minutes if you carry the structure $F \propto \sigma m^2 v$ as a memorized skeleton and read each part off it — the strength-enters-twice step is the planted trap, with $v_0/2$ waiting as the wrong option. Deriving the chain from scratch mid-exam costs five minutes; owning it costs none.

Exam traps

Who examines this — read before revising. CBSE's 2025-26 syllabus no longer names eddy currents: the 2023 rationalization removed them, and they have not returned (this module keeps the CB tag for continuity with NCERT-based teaching, but check your current year's list). JEE-Main and NEET both name "eddy currents" explicitly in their EMI units; ISC demands them "(qualitative)". JEE-Advanced, A-Level (9702), IB and IGCSE do not list them at all — for those exams this is enrichment, not syllabus.

"Copper is attracted because it becomes magnetic." No — the pipe grips the magnet only while flux changes. Material magnetism (dia/para/ferro) persists at rest; eddy effects die with the motion. The warning box carries the full autopsy.

Eddies treated as always harmful. Half the applications table is deliberate exploitation. "State two applications and one disadvantage" wants brakes/furnace/damping and core losses — pick from both columns.

Lamination explained backwards. The sheets must lie parallel to the flux so they cut the eddy loops, which swirl perpendicular to it. "Lamination blocks the magnetic field" is a zero — the flux passes exactly as before; only the current paths are chopped.

Drag that survives at rest. Eddy braking force is proportional to speed: it vanishes at $v = 0$ . A design relying on eddy drag to hold something stationary fails; it can only slow things. (This is why eddy brakes on trains are paired with friction brakes for the final stop.)

Magnet strength counted once. In any eddy-drag scaling, the source's strength enters twice — creating the flux and feeling the reaction. Ratio MCQs plant the once-counted answer.

Direction guessed instead of derived. Every eddy direction question is Lenz's four-step algorithm on the loop nearest the change — run it, name the faces (as in the pipe derivation), collect the marks.

Boards and constants. Numerical eddy questions are estimates — order-of-magnitude answers with stated assumptions score full marks (as in the board example). Where weights appear, $g = 9.8$ m/s² for CBSE/NEET, 10 for JEE quick math.

Origins · 1 minLéon Foucault and how this was discovered

Léon Foucault

1819–1868 · Paris

Foucault trained for medicine and fled it — he fainted at the sight of blood — into a life of ingenious measurement. In 1855 he mounted a copper disc between the poles of an electromagnet and spun it: with the magnet off, the disc coasted freely; energized, it braked hard and grew warm, dissipation with no contact whatsoever. That warming disc closed a thirty-year-old case: Arago had found in 1824 that a spinning copper disc mysteriously dragged a compass needle along, magnetism from unmagnetizable metal that baffled everyone until Faraday identified induction at work; Foucault's experiment completed the energy ledger — braking work in, heat out — and France still calls eddy currents courants de Foucault. The same restless hands measured the speed of light to better than one percent with a rotating mirror, invented the gyroscope, and devised the knife-edge test opticians still use on telescope mirrors. (The pendulum bearing his name, which showed the Earth itself turning beneath Paris in 1851, belongs to the mechanics track's story.) He died at 48, having made more invisible things visible than almost any experimenter of his century.

History

1824

— Arago's rotating copper disc drags a compass needle: eddy physics observed before induction is understood.

1831

— Faraday identifies Arago's mystery as electromagnetic induction in bulk metal.

1855

— Foucault's disc experiment: braking plus heating, the energy ledger closed, the currents named.

1892

— Steinmetz separates machine-core losses into hysteresis and eddy shares, arming transformer designers.

1900

s — laminated silicon-steel cores become universal; the grid's transformers stop cooking themselves.

1979

— eddy-current crack testing is standardized for aircraft skins: the foe re-hired as an inspector.

Going further

Texts. NCERT Physics Class 12, Ch. 6 (§6.8, retained in the rationalized text as reading) · HC Verma Vol. 2, Ch. 38 · SL Arora, ISC Physics XII, electromagnetic induction (eddy currents, qualitative).

Provenance. All results standard; numerical estimates are order-of-magnitude by design. A verifier should recompute: disc-loop estimate $\varepsilon = 0.30 \times \pi(0.05)^2 \times 314 = 0.74$ V and $P = (0.74)^2/1.1\times10^{-4} \approx 5$ kW; pipe timings $0.50/0.045 \approx 11$ s versus $\sqrt{2\times0.50/9.8} = 0.32$ s; conductivity ratio $\sigma_{\text{Cu}}/\sigma_{\text{Al}} \approx 5.9/3.5 \approx 1.7$ setting the terminal-speed ratio.

Prerequisites. Lenz's Law & Energy Conservation · Faraday's Law of Induction · Magnetic Flux. Leads to. Flux-Change Numericals — Pulls, Flips & Ramps (coming in this chapter's gym) · The Transformer (coming in the AC chapter) · Eddy Currents (UG deep dive).

If copper's susceptibility is basically zero, how can a magnet exert such a strong force on it?

Two different experiments hide in the word "force". Hold the magnet still near copper and the force really is negligible — diamagnetism at χ ≈ −10⁻⁵ is beyond feeble; that is the material response the classification drill measures. Move the magnet, and you switch on a completely different mechanism: the changing flux induces circulating currents, and those currents are genuine electromagnets — their strength set by the speed of the change and the metal's conductivity, not by χ at all. The grip can be strong enough to slow a fall a thirty-fold, yet it dies the instant relative motion stops. Quick test to keep them straight: material magnetism persists at rest; eddy forces exist only during change.

Where exactly does the falling magnet's lost energy go?

Into heat in the pipe wall — through honest bookkeeping. Falling at terminal speed, the magnet loses gravitational energy $mgh$ over a drop $h$ but gains no kinetic energy; every joule is spent driving ring currents against the copper's resistance, warming it. The amounts are small but real: a 50-gram magnet crawling down half a metre deposits about $0.05 \times 9.8 \times 0.5 \approx 0.25$ J in the pipe. Foucault's 1855 disc showed the same ledger at measurable scale — the disc braked and warmed together. Lenz's law is what guarantees the ledger balances this way: induced effects always consume mechanical energy; a pipe that sped the magnet up would be manufacturing energy from nothing.

Why does slitting the pipe lengthwise kill the effect, when almost all the copper is still there?

Because eddy currents need closed loops, and the natural loops in a pipe are its circular rings — every one of which the lengthwise slit interrupts. The emf is still induced; the charges are still pushed; but a pushed charge arriving at the slit has nowhere to go, so no circulating current builds up beyond a trace of local swirling. Mass is irrelevant; topology is everything. This is precisely the principle scaled down in laminated cores (insulated sheets = many slits) and in the classic slotted-pendulum demo, where a comb-shaped copper plate swings almost freely between magnet poles while its solid twin stops dead in one pass.

Why does an induction cooktop need special pans, and why does the glass stay cool?

The cooktop's coil drives a rapidly alternating flux upward into the pan base; eddies swirl in the metal and heat it directly — the pan is the heating element. The glass stays cool because it is an insulator: plenty of changing flux, no mobile charges, no current, no heat (it warms only by contact with the hot pan). Pan choice is the classification drill in daily life: a ferromagnetic base (iron, many stainless steels) concentrates the flux and heats fiercely; plain aluminium or copper couples so weakly at cooktop frequencies that most units refuse to switch on. That is why induction-ready cookware is marked, and why a magnet sticking to the base is the shopper's quick test.

Do eddy currents only happen when something moves?

No — motion is just one way to change flux. A perfectly stationary transformer core at 50 Hz hosts eddies all day, because the field itself alternates; the stationary pan on a cooktop heats the same way. Moving cases (brakes, the pipe demo, Arago's disc) are the theatrical ones because they produce visible forces, but the underlying rule is only ever equation (1): any flux change, whatever its cause, drives whirlpools in whatever conductor it threads. That unification — motion-made and field-made flux change obeying one law — is exactly the master statement of Faraday's Law of Induction.

Is the "dead-beat" galvanometer really the same physics as a train brake?

Identical, at a thousandth the scale. A galvanometer needle on a spring would naturally overshoot and oscillate around its reading. Winding the coil on a light metal former fixes it: as the former swings through the radial field, its flux changes, eddies swirl, and Lenz-drag opposes the swing — strong when the needle moves fast, zero once it settles. The needle glides to its reading and stops: "dead-beat". It is the train-brake curve (drag ∝ speed, vanishing at rest) exploited for settling rather than stopping — and the reason your practical-exam galvanometer doesn't waste your time wobbling. The Moving-Coil Galvanometer notes this damping hook in its anatomy.