en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T13:28:39Z

References: replace mr template with mr parameter in CS1 templates; using AWB

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139.218.218.86: not a number field . . .

2014-02-09T03:45:45Z

not a number field . . .

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en>Tariqabjotu: Tariqabjotu moved page Lasker–Noether theorem to Primary decomposition: per move request

2013-08-24T02:07:07Z

Tariqabjotu moved page Lasker–Noether theorem to Primary decomposition: per move request

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{{Electromagnetism|cTopic=Electrostatics}}
In [[electromagnetism]], '''electric flux''' is the rate of flow of the [[electric field]] through a given area. Electric flux is proportional to the number of electric [[field line]]s going through a virtual surface. If the electric field is uniform, the electric flux passing through a surface of [[vector area]] {{math|'''S'''}} is
:<math>
\Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta,
</math>
where {{math|'''E'''}} is the electric field (having units of {{math|V/m}}), {{math|''E''}} is its magnitude, {{math|''S''}} is the area of the surface, and {{math|''θ''}} is the angle between the electric field lines and the normal (perpendicular) to {{math|''S''}}. For a non-uniform electric field, the electric flux {{math|''d''Φ'''''E'''''}} through a small surface area {{math|''d'''''S'''}} is given by
:<math>d\Phi_E = \mathbf{E} \cdot d\mathbf{S}</math>
(the electric field, {{math|'''E'''}}, multiplied by the component of area perpendicular to the field). The electric flux over a surface {{math|''S''}} is therefore given by the [[surface integral]]:
:<math>\Phi_E = \iint_S \mathbf{E} \cdot d\mathbf{S}</math>
where {{math|'''E'''}} is the electric field and {{math|''d'''''S'''}} is a differential area on the closed surface {{math|''S''}} with an outward facing [[surface normal]] defining its direction.

For a closed [[Gaussian surface]], electric flux is given by:
:{{oiint
| preintegral = <math>\Phi_E =\,\!</math>
| intsubscpt = <math>\scriptstyle S</math>
| integrand = <math>\mathbf{E}\cdot d\mathbf{S} = \frac{Q}{\epsilon_0}\,\!</math>}}

where
:{{math|'''E'''}} is the [[electric field]],
:{{math|''S''}} is any [[closed surface]],
:{{math|''Q''}} is the total [[electric charge]] inside the surface {{math|''S''}},
:{{math|''ε''0}} is the [[electric constant]] (a universal constant, also called the "[[permittivity]] of free space") (ε0 ≈ 8.854 187 817... x 10−12 [[farad]]s per [[meter]] (F·m−1)).
This relation is known as [[Gauss' law]] for electric field in its [[integral]] form and it is one of the four [[Maxwell's equations]].

It is important to note that while the electric flux is not affected by charges that are not within the closed surface, the net electric field, {{math|'''E'''}}, in the Gauss' Law equation, can be affected by charges that lie outside the closed surface. While Gauss' Law holds for all situations, it is only useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry.

Electrical flux has [[SI]] units of [[volt]] [[metre]]s ({{math|''V m''}}), or, equivalently, [[newton (unit)|newton]] metres squared per [[coulomb]] ({{math|''N m''2 ''C''−1}}). Thus, the [[SI]] base units of electric flux are {{math|''kg·m''3''·s''−3''·A''−1}}.

Its dimensional formula is {{math|[L3MT–1I–1]}}.

==See also==
*[[Magnetic flux]]
*[[Maxwell's equations]]

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

[[Category:Electrostatics]]
[[Category:Physical quantities]]

Primary decomposition - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

139.218.218.86: not a number field . . .

en>Tariqabjotu: Tariqabjotu moved page Lasker–Noether theorem to Primary decomposition: per move request