Lenz's law of induction
Statement
The induced current in a closed loop always flows in the direction such that its own magnetic field opposes the flux change that created it — mathematically this is the "−" sign in Faraday's ε = −dΦ/dt.
Why is it true?
If the induced current flowed the other way, its field would amplify the flux change rather than oppose it — producing an infinitely self-amplifying process and violating energy conservation. The minus sign is the universe's safety mechanism.
Lenz explained Faraday's "−" sign three years later (1834). It's also why a magnet dropped through a copper tube falls slowly — the induced currents create a braking force.
Applications
Electromagnetic braking in high-speed trains and bicycles, inductive position sensors, induction cooktops, eddy-current dampers for bridges, railguns and generators.
Stated by
Topics that use this theorem
Related theorems
Step-by-step proofs