Faraday's Law

Definition

The rule that a changing magnetic field creates electricity — the principle behind every generator and transformer.

ε=−NdΦdt\varepsilon = -N\frac{d\Phi}{dt}

Unit: V (EMF)

Technical definition

The induced electromotive force around a closed loop equals the negative rate of change of magnetic flux through it: ε = −N·dΦ/dt. One of Maxwell's equations; the negative sign (Lenz's law) enforces energy conservation.

Example

Spinning a coil at 60 revolutions per second in a magnetic field makes the flux oscillate — inducing the 60 Hz alternating voltage of the power grid.

Common confusion

It is the CHANGE in flux that matters, not the flux itself. A huge steady magnetic field induces nothing; a tiny field flipping rapidly can induce a large voltage. Students often forget the time derivative.