Thomson's Jumping Ring: How a Coil Launches a Metal Ring

The Demonstration: A Coil That Fires a Ring

The apparatus is deceptively simple: a vertical solenoid of hundreds to a thousand turns wound around a tall soft-iron core, fed from the AC mains (120–240 V, 50/60 Hz). Slip a light aluminum ring over the core so it rests near the bottom, throw the switch, and the ring leaps upward — a modest ring hops half a metre, a well-tuned rig sends it to the ceiling. Leave the current on and a heavier ring can be made to hover, floating in mid-air on nothing but a magnetic field while it slowly warms up.

Two control experiments reveal the mechanism at a glance. Cut a thin slit through the ring so no current can circulate, and it refuses to jump — it just sits there. Cool a solid ring in liquid nitrogen first, and it jumps dramatically higher. Both facts are the physics telling you what matters: a complete conducting loop, and its electrical resistance.

The Causal Chain: Faraday, Lenz, and the Radial Field

Step by step, here is why the ring flies:

1. Changing flux. The AC coil current makes the iron core's magnetic field rise and fall. The flux Φ threading the ring changes with it.
2. Induced EMF. By Faraday's law, EMF = −dΦ/dt. A changing flux drives a voltage around the ring.
3. Induced current. That EMF pushes a large current around the low-resistance ring — hundreds to over a thousand amperes at peak.
4. Lenz opposition. By Lenz's law the ring's current flows so as to oppose the rising flux; the ring becomes a little electromagnet whose face points the same way as the coil's — like poles facing, so they repel.
5. The radial field does the lifting. Near the top of the iron core the field lines splay outward, so at the ring there is a radial component B_r as well as the vertical one. The vertical Lorentz force on the ring's azimuthal current I is F = 2πa · I · B_r, where a is the ring radius. That outward-leaning field, not the vertical field, is what launches the ring.

The vertical part of the field, crossed with the same current, only squeezes the ring inward radially — it never lifts. This is the point most short explanations skip.

Why It Needs AC: The All-Important Phase Lag

Here is the beautiful subtlety. Write the coil's field as B(t) ∝ cos ωt. Then EMF ∝ −dB/dt ∝ sin ωt. The ring is not a pure resistor — it has inductance L — so its current lags the EMF by an angle φ with tan φ = ωL/R, giving I(t) ∝ sin(ωt − φ).

The instantaneous force follows the product F(t) ∝ I(t)·B(t) ∝ sin(ωt − φ)·cos ωt. Average that over a cycle and everything cancels except one term: ⟨F⟩ ∝ sin φ. So the time-averaged lift is proportional to the phase lag. If the ring were a perfect resistor (φ = 0), the current would sit exactly 90° out of phase with the field and the average force would be zero — the ring would buzz at 120 Hz and warm up but never rise. It is the ring's inductance that tilts the timing and turns a wobble into a launch.

This also explains the liquid-nitrogen trick. Cooling aluminum roughly halves its resistance for every ~130 K drop; lowering R both increases the current magnitude and increases φ (larger ωL/R), so ⟨F⟩ climbs on both counts. A ring that hopped now hits the ceiling.

A Worked Estimate: How Hard Is the Kick?

Take an aluminum ring of radius a ≈ 3 cm and cross-section ~15 mm² (mass ≈ 8 g, weight ≈ 0.08 N). Suppose the peak axial field in the core is B ≈ 0.4 T. The peak flux through the ring is Φ ≈ B·πa² ≈ 0.4 × π(0.03)² ≈ 1.1×10⁻³ Wb.

The peak EMF at 60 Hz is EMF ≈ ωΦ ≈ 377 × 1.1×10⁻³ ≈ 0.42 V. The ring's resistance is tiny — for aluminum, R = ρL/A ≈ 2.8×10⁻⁸ × 0.19 / 1.5×10⁻⁵ ≈ 3.5×10⁻⁴ Ω — so the circulating current is of order I ~ 10³ A (somewhat reduced by reactance).

With a radial field of, say, B_r ≈ 0.05 T at the ring, the lift is F ≈ 2πa · I · B_r ≈ 0.19 × 800 × 0.05 ≈ 8 N. Against an 0.08 N weight that is F/W ≈ 100, i.e. an acceleration near 100 g and a launch in a few milliseconds. These are order-of-magnitude figures — real values depend on core saturation, the ring's height on the core, and reactance — but they show why the effect is so violent.

Subtleties and the Misconception Everyone Trips On

The misconception: that the strong vertical field lifts the ring. It cannot — a vertical B crossed with the ring's horizontal current points radially inward, compressing the ring, not raising it. The lift comes entirely from the smaller radial field where the lines fan out near the core's top, which is exactly why the iron core matters: it both multiplies the flux (high permeability) and shapes the field so it leans outward. Remove the core and the jump nearly vanishes.

Does DC work? Only for an instant. Switch DC on and the switch-on transient (a one-off dΦ/dt) gives a single kick; once the current is steady, dΦ/dt = 0, no induced current, no force. Sustained lift and levitation need AC (or repeated pulses).

The slit ring proves the loop must be closed: cut it and the induced current has nowhere to circulate, so no magnetic moment and no force. And the ring genuinely does heat up — the same I²R that limits the current dumps real power, which is why a hovering ring eventually falls as it warms and its resistance climbs.

From Lecture Bench to Induction Motors and Coilguns

Elihu Thomson — the American engineer and co-founder of the firm that became General Electric — showed this trick in the late 1880s, and it has been a physics-classroom staple ever since. But the same induced-current repulsion runs a great deal of technology. Swap the geometry and the ring's azimuthal current becomes the rotor current of an induction motor, where the Lenz-law interaction produces torque instead of lift. Push the field pulse to extremes with a capacitor discharge and the jumping ring becomes an electromagnetic launcher or coil-gun stage, flinging a ring or armature at high speed.

The dissipative cousin — a conductor moving through a field, its eddy currents opposing the motion — is the eddy-current brake on trains and roller coasters. And the extreme low-resistance limit points at superconductors: a superconducting ring (R → 0, φ → 90°) is the strongest jumper of all, the same physics that levitates a magnet over a cooled superconductor. Induction cooktops and induction heating are the jumping ring with the mechanical launch removed and only the I²R heating kept.

Three faces of the same Faraday–Lenz induced-current force

Feature	Thomson's jumping ring	Eddy-current brake	Induction motor
Source field	AC solenoid with iron core	Magnet or conductor in relative motion	Rotating stator field
Induced current in	Aluminum ring (azimuthal loop)	Solid conductive disc or rail	Rotor cage bars
Net effect	Axial repulsion → ring launches	Drag opposing motion → braking	Tangential torque → rotation
What Lenz opposes	The rising flux through the ring	The relative motion	The slip between field and rotor
Key requirement	Ring inductance (phase lag) + radial B	Relative velocity	Slip between field and rotor speed
Everyday example	Physics demo, coil launchers	Train & roller-coaster brakes	Washing-machine & fan motors