Gauss's law: Difference between revisions
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The electric flux Φ<sub>''E''</sub> is defined as a surface integral of the electric field: | The electric flux Φ<sub>''E''</sub> is defined as a surface integral of the electric field: | ||
oiint|preintegral=<math>\Phi_E = </math>|intsubscpt=<math>{\scriptstyle S}</math>|integrand=<math>\mathbf{E} \cdot \mathrm{d}\mathbf{A}</math> | |||
where '''E''' is the electric field, d'''A''' is a vector representing an [[infinitesimal]] element of [[area]],{{refn|More specifically, the infinitesimal area is thought of as [[Plane (mathematics)|planar]] and with area d''A''. The vector d'''A''' is [[Normal (geometry)|normal]] to this area element and has [[magnitude (vector)|magnitude]] d''A''.<ref>{{cite book|last=Matthews|first=Paul|title=Vector Calculus|publisher=Springer|year=1998|isbn=3-540-76180-2}}</ref>|group=note}} and · represents the [[dot product]] of two vectors. | where '''E''' is the electric field, d'''A''' is a vector representing an [[infinitesimal]] element of [[area]],{{refn|More specifically, the infinitesimal area is thought of as [[Plane (mathematics)|planar]] and with area d''A''. The vector d'''A''' is [[Normal (geometry)|normal]] to this area element and has [[magnitude (vector)|magnitude]] d''A''.<ref>{{cite book|last=Matthews|first=Paul|title=Vector Calculus|publisher=Springer|year=1998|isbn=3-540-76180-2}}</ref>|group=note}} and · represents the [[dot product]] of two vectors. | ||
Revision as of 16:19, 29 November 2015
To be continued by Tony Chen wchen408
Topic Description
Gauss's law is a method to determine the electric field for situations where the charges are contained in a closed surface. Gauss's law relates charges distribution with the concept of electric flux, which is essentially the amount of an electric field passing through a surface. [math]\displaystyle{ \Phi_E = \mathbf{E} \cdot \mathrm{d}\mathbf{A}\cos\Theta }[/math]. Gauss's law is always true, but for physics 2, it becomes only when calculating the electric field in situations with sufficient symmetry:
]
Qualitative description
The electric flux that passes through a closed surface can be found by adding up all the charges enclosed by the closed surface divided by the constant ε0; or by adding up all the electric field on the gaussian surface dot dA(the infinitesimal surface area). As illustrate by the equation : [math]\displaystyle{ \Phi_E = \frac{Q}{\varepsilon_0} }[/math], where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total electric charge enclosed within S, and ε0 is the electric constant. T
Integral Form
The electric flux ΦE is defined as a surface integral of the electric field:
oiint|preintegral=[math]\displaystyle{ \Phi_E = }[/math]|intsubscpt=[math]\displaystyle{ {\scriptstyle S} }[/math]|integrand=[math]\displaystyle{ \mathbf{E} \cdot \mathrm{d}\mathbf{A} }[/math]
where E is the electric field, dA is a vector representing an infinitesimal element of area,Template:Refn and · represents the dot product of two vectors.
Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.
A VPython Model
Visualizing Gauss's Law in Vpython Model, consider embedding some vpython code here Python Demo By Matter & Interactions 4e
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