Faraday's law of induction

Faraday's law of induction (more generally, the law of electromagnetic induction) states that a magnetic field changing in time creates a proportional electromotive force.

The relation between the rate of change of the magnetic flux through the surface S enclosed by a contour C and the electric field along the contour:

\oint_C \mathbf{E} \cdot d\mathbf{l} = - \ { d \over dt }   \int_S   \mathbf{B} \cdot d\mathbf{A}

where E is the electric field, dl is an infinitesimal element of the contour C and B is the magnetic flux density. The directions of the contour C and of $d\mathbf{A}$ are assumed to be related by the right-hand rule.

Equivalently, the differential form of Faraday's law is

\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}

which is one of the Maxwell equations.

In the case of an inductor coil where the electric wire makes N turns, the formula becomes:

V=-N{d \Phi \over d t}

where V is the induced electromotive force and dΦ/dt is the time-rate of change of magnetic flux Φ. The direction of the electromotive force (the negative sign in the above formula) was first given by Lenz's law.

Faraday's law, along with the other laws of electromagnetism, was later incorporated into Maxwell's equations, unifying all of electromagnetism.

Faraday's law of induction is based on Michael Faraday's experiments in 1831.

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