Gauss's law: Difference between revisions
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:<math>\Phi_E = \frac{Q}{\varepsilon_0}</math> | :<math>\Phi_E = \frac{Q}{\varepsilon_0}</math> | ||
where Φ<sub>''E''</sub> is the [[electric flux]] through a closed surface ''S'' enclosing any volume ''V'', ''Q'' is the total | where Φ<sub>''E''</sub> is the [[electric flux]] through a closed surface ''S'' enclosing any volume ''V'', ''Q'' is the total electric charge enclosed within ''S'', and ''ε''<sub>0</sub> is the electric constant. 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>}} | :{{oiint|preintegral=<math>\Phi_E = </math>|intsubscpt=<math>{\scriptstyle S}</math>|integrand=<math>\mathbf{E} \cdot \mathrm{d}\mathbf{A}</math>}} | ||
Revision as of 13:19, 29 November 2015
Claimed --User:Wchen408 14:50, 5 November 2015 (EST)
Short Description of Topic
A metal bar moving through a magnetic field will polarize as a result of magnetic force, and the resulting charge separation, maintained by the magnetic force, is reminiscent of a battery. The polarized bar can then be used to generate an electric current.
Qualitative description
Gauss's law is for finding electric field. 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]
Integral Form
Gauss's law may be expressed as:
- [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. 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.
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