LenzorLenz’s Law / Eddy-Current BrakingSticker

Lenzor is a copper pipe with a contrarian streak.

Drop a strong magnet down him and it does not fall like a stone. It drifts down as if through syrup, though copper is not magnetic and nothing touches the magnet. The answer is induction. As the magnet approaches a ring of the pipe, the magnetic flux through that ring grows; as it leaves, the flux shrinks. Michael Faraday found in 1831 that a changing flux drives a current. In 1834 the Russian physicist Heinrich Lenz gave the rule for its direction: the induced current always flows so as to oppose the change that made it. That opposition is the minus sign in the first line on this page.

So Lenzor pushes back. Below the falling magnet, a ring builds a pole that repels it; above, a ring circulating the other way clings on and pulls. Eddy currents swirl round the pipe just ahead of the magnet and just behind it.

But he can’t stop it. His push exists only while the magnet moves, and it grows with the speed. The magnet speeds up until the drag matches its weight, then falls at a slow, steady terminal speed: the second line. The energy it loses on the way down does not vanish and is not stored; it ends up as heat in the copper. In 1993 MacLatchy, Backman and Bogan turned this magnetic braking into a quantitative student experiment.

The rule is energy bookkeeping. If the induced current helped the change instead of opposing it, the magnet would be pulled along for free while the copper warmed, and energy would not be conserved. Opposition is his whole personality, which is exactly what the minus sign means.

Change the flux. I push back.