The Faraday-Neumann law contains a minus sign that at first glance looks like a detail. It is not: it is Lenz’s law, and it embodies a principle of energy conservation.
If the sign were positive, the induced current would tend to reinforce the flux change that caused it, triggering a self-amplifying process: a small disturbance would grow without limit, and one could extract energy from nothing. The minus sign, instead, says that the induced current opposes the cause: it behaves like an “electromagnetic friction” that requires external work to overcome.
This is why a magnet falling through a copper tube slows down: the kinetic energy lost by the magnet does not vanish, it is converted into heat by the Joule effect in the induced currents. The minus sign is, in essence, the electromagnetic translation of the first law of thermodynamics (Battimelli and Stilli 1999; Feynman, Leighton and Sands 1963). See also Riferimenti bibliografici.
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Topics: Electromagnetic induction Concepts: Lenz’s law · Faraday-Neumann-Lenz law
Related exercises: Worked exercise — loop entering and leaving a field · Problem — Loop entering a field (qualitative) · Problem — Induced EMF over time (graph)