Editing Magnetic flux (section)

== Changing magnetic flux ==
{{Main|Faraday's law of induction}}
For example, a change in the magnetic flux passing through a loop of conductive wire will cause an [[electromotive force]] (emf), and therefore an electric current, in the loop.  The relationship is given by [[Faraday's law of induction|Faraday's law]]:
<math display="block">\mathcal{E} = \oint_{\partial \Sigma} \left( \mathbf{E} + \mathbf v \times \mathbf B\right) \cdot d\boldsymbol{\ell} = -\frac{d\Phi_B}{dt},</math>
where:
*<math>\mathcal{E}</math> is the electromotive force ([[electromotive force|EMF]]), 
* The minus sign represents Lenz's Law,
*{{math|Φ<sub>''B''</sub>}} is the magnetic flux through the open surface {{math|Σ}},
*{{math|∂Σ}} is the boundary of the open surface {{math|Σ}}; the surface, in general, may be in motion and deforming, and so is generally a function of time. The electromotive force is induced along this boundary.
*{{math|''d'''ℓ'''''}} is an [[infinitesimal]] vector element of the contour {{math|∂Σ}},
*{{math|'''v'''}} is the velocity of the boundary {{math|∂Σ}},
*{{math|'''E'''}} is the [[electric field]], and
*{{math|'''B'''}} is the [[magnetic field]].

The two equations for the EMF are, firstly, the work per unit charge done against the [[Lorentz force]] in moving a test charge around the (possibly moving) surface boundary {{math|∂Σ}} and, secondly, as the change of magnetic flux through the open surface {{math|Σ}}. This equation is the principle behind an [[electrical generator]].
{{Clear}}
[[File:Spulenflaeche.jpg|thumb|center|300px|Area defined by an electric coil with three turns.]]
{{Clear}}