Gauss's law: Difference between revisions
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===Topic Description=== | ===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>\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:[[File:Flux_Sphere.JPG]] | 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>\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:[[File:Flux_Sphere.JPG|200px|thumb|right|Flux_Sphere]]] | ||
===Qualitative description=== | ===Qualitative description=== | ||
Revision as of 14:19, 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:
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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