View source for Electric flux

{{Electromagnetism|cTopic=[[Electrostatics]]}}
Imagine an electric field E passing through a surface. Consider an [[infinitesimal]] area (dA) on that surface across which E remains constant. Also assume that the angle between E and dA is i. The electric flux is defined as EdAcos(i). E and dA are vectors. Flux is the [[dot product]] of E and dA. Using full [[vector]] notation, the electric flux <math>d\Phi_E\,</math> through a small area <math>d\mathbf{A}</math> is given by
:<math>d\Phi_E = \mathbf{E} \cdot d\mathbf{A}</math>

The electric flux over a surface ''S'' is therefore given by the [[surface integral]]:
:<math>\Phi_E = \int_S \mathbf{E} \cdot d\mathbf{A}</math>
where '''E''' is the electric field and d'''A''' is a differential area on the surface <math>S</math> with an outward facing [[surface normal]] defining its direction. 

For a closed [[Gaussian surface]], electric flux is given by:
:<math>\Phi_E = \oint_S \mathbf{E} \cdot d\mathbf{A} = \frac{Q_S}{\epsilon_0}</math>
where Q<sub>S</sub> is the net [[Electric charge|charge]] enclosed by the surface (including both [[free charge|free]] and [[bound charge]]), and ε<sub>0</sub> is the [[electric constant]]. This relation is known as [[Gauss' law]] for electric field in its [[integral]] form and it is one of the four [[Maxwell's equations]].

Electric flux is not affected by charges that are not within the closed surface. But the net electric field, '''E''', in the Gauss' Law equation, can be affected by charges that lie outside the closed surface.  Gauss' Law is true in all situations, but people can only use it to calculate when high degrees of symmetry exist in the electric field.  Examples include spherical and cylindrical symmetry. Otherwise, the calculations are too hard to do by hand and must be worked out using a [[computer]].

Electrical flux has [[SI]] units of [[volt]] metres (V m), or, equivalently, [[newton (unit)|newton]] metres squared per [[coulomb]] {{nowrap|(N m<sup>2</sup> C<sup>−1</sup>)}}. So, the SI base units of electric flux are kg•m<sup>3</sup>•s<sup>−3</sup>•A<sup>−1</sup>.

==Related pages==
*[[Magnetic flux]]

== Other websites ==
* [http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/gaulaw.html#c3 Electric flux] — [[HyperPhysics]]


[[Category:Electromagnetism]]