Eddy Currents: Braking a Magnet With Nothing But Induction

Faraday's law, applied inside a solid conductor

Faraday's law of induction says any change in magnetic flux through a conducting loop induces an electromotive force around that loop: EMF = −dΦ/dt. Usually you picture this with a wire loop, but a solid block of metal is, electrically, an infinite collection of overlapping loops. When a magnet falls past a conducting tube, the flux through every one of those imaginary loops changes as the magnet approaches and then recedes, and each loop responds with its own induced current. These swirling, closed loops of current inside the bulk of the conductor are eddy currents.

Lenz's law: the current always opposes the change

Lenz's law fixes the direction of every induced current: it flows so as to oppose the change in flux that created it, a direct consequence of energy conservation — if it reinforced the change instead, you would get free energy from nothing. As the magnet approaches a ring of the tube, the induced eddy current creates its own magnetic field that repels the magnet; as the magnet recedes, the current reverses and now creates a field that attracts it back. Both effects act like a drag force that always opposes the magnet's motion, whatever direction it happens to be moving in — which is why this is called magnetic braking rather than magnetic repulsion or attraction.

EMF   = -d(Phi)/dt              // Faraday's law
F_eddy ~ -k * v                 // braking force proportional to velocity (low-speed limit)
k     ~ B^2 * sigma * t / rho   // depends on field strength, conductivity, tube thickness

Why the material matters so much

The braking force scales with the material's electrical conductivity σ, because a more conductive metal lets larger eddy currents flow for the same induced EMF, and those larger currents create a stronger opposing field. Copper (σ ≈ 5.96×10⁷ S/m) and aluminium (σ ≈ 3.5×10⁷ S/m) are excellent conductors and brake a falling magnet dramatically — a magnet dropped through a thick copper pipe can take several seconds to emerge instead of a fraction of a second in free fall. Steel conducts electricity reasonably well too, but its high magnetic permeability and (for common alloys) lower conductivity than copper give a different, often weaker braking profile, and plastic and other insulators have essentially no free charge carriers to form eddy currents at all, so a magnet falls through a plastic tube exactly as if the tube were not there.

Where the energy goes: resistive (I²R) heating

Eddy currents do not disappear the magnet's kinetic energy by magic — they convert it into heat through ordinary resistive dissipation, I²R, distributed through the volume of the conductor as those circulating currents fight the metal's own electrical resistance. This is the same physical mechanism that makes induction cooktops work: an alternating magnetic field induces eddy currents directly in the base of a ferromagnetic pan, and the pan's own resistance heats the food, with no red-hot heating element anywhere. It is also why transformer cores and motor laminations are built from thin, electrically insulated sheets rather than a solid block of iron — thin laminations interrupt the loops that eddy currents would otherwise trace, cutting wasted heat while leaving the desired magnetic flux path largely intact.

Terminal velocity, not free fall

Because the braking force in the simple regime grows linearly with velocity (Lenz's law resisting whatever speed the magnet currently has), a magnet falling through a long conducting tube quickly reaches a terminal velocity where the eddy-current drag exactly balances gravity, much like a skydiver reaching terminal velocity against air resistance — except here the medium is solid metal and the resistance is electromagnetic rather than aerodynamic. This is also the mechanism behind real eddy-current brakes used in some trains and roller coasters: a set of magnets moves close to a conductive rail or disc with no physical contact at all, and the braking force appears purely from induced currents, wearing out no brake pads and needing no friction surface.

Frequently asked questions

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