The Faraday–Lenz law of electromagnetic induction

Statement

$\varepsilon = -N\dfrac{d\Phi}{dt}$ — the EMF induced in a closed loop is proportional to the rate of change of magnetic flux $\Phi$ through it ($N$ is the number of turns); the minus sign (Lenz) shows the induced current always opposes the change that created it.

Why is it true?

Faraday found the magnitude part experimentally (1831); Lenz added the rule for the induced current's direction, itself a consequence of energy conservation — if the induced current reinforced the flux instead of opposing it, energy would be created from nothing.

Topics that use this theorem

Step-by-step proofs

No step-by-step proof yet for this theorem.