Electric Flux: Difference between revisions
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Electric flux through an area is the electric field multiplied by the area of a plane that is perpendicular to the field. Gauss's Law | Electric flux through an area is the electric field multiplied by the area of a plane that is perpendicular to the field. Gauss's Law relates the electric flux through an area to the amount of charge enclosed in that area. Gauss's law must be used along a closed surface, but any chosen surface that contains the same amount of charge will give the same answer | ||
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<math display="block">\text {Electric Flux:} Φelectric= \int \ {\vec{E}cosθdA} </math> | <math display="block">\text {Electric Flux:} Φelectric= \int \ {\vec{E}cosθdA} </math> | ||
Where theta is the angle between the electric field vector and the surface normal. | Where theta is the angle between the electric field vector and the surface normal. | ||
Combining these two equations | Combining these two equations gives: | ||
<math display="block">\text{Gauss's Law for Electric Fields:} \oint{ \vec{E} \cdot d\vec{A} } ⃗= {Q\over ε_0} </math> | <math display="block">\text{Gauss's Law for Electric Fields:} \oint{ \vec{E} \cdot d\vec{A} } ⃗= {Q\over ε_0} </math> | ||
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References | References | ||
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c1 | |||
Revision as of 20:04, 30 November 2015
The Main Idea
Electric flux through an area is the electric field multiplied by the area of a plane that is perpendicular to the field. Gauss's Law relates the electric flux through an area to the amount of charge enclosed in that area. Gauss's law must be used along a closed surface, but any chosen surface that contains the same amount of charge will give the same answer
A Mathematical Model
[math]\displaystyle{ \text{Electric Flux:} Φelectric ={ Q \over ε_0} }[/math]
[math]\displaystyle{ \text {Electric Flux:} Φelectric= \int \ {\vec{E}cosθdA} }[/math]
Where theta is the angle between the electric field vector and the surface normal.
Combining these two equations gives:
[math]\displaystyle{ \text{Gauss's Law for Electric Fields:} \oint{ \vec{E} \cdot d\vec{A} } ⃗= {Q\over ε_0} }[/math]
A Computational Model
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References http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c1