Gauss's LawGausssLaw2006-12-17 21:51:432006-12-17 21:51:43DefinitionAdded electric displacement with Gauss's law.% this is the default PlanetPhysics preamble. as your knowledge
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% define commands here\subsection{Introduction}
Gauss's law, one of Maxwell's equations, gives the relation between the electric or gravitational flux flowing out a closed surface and, respectively, the electric charge or mass enclosed in the surface. It is applicable whenever the inverse-square law holds, the most prominent examples being electrostatics and Newtonian gravitation.
If the system in question lacks symmetry, then Gauss's law is inapplicable, and integration using Coulomb's law is necessary.
\subsection{Definition (Integral form)}
In its integral form, Gauss's law is
\begin{displaymath}
\Phi = \oint_S \vec{E} \cdot \,\vec{dA} = \frac{1}{\epsilon_0}\int_V \,dV = \frac{q_{enc}}{\epsilon_0}
\end{displaymath}
where $\Phi$ is electric flux, $S$ is some closed surface with outward normals, $\vec{E}$ is the electric field, $\vec{dA}$ is a differential area element, $\epsilon_0$ is the permittivity of free space, $q_{enc}$ is the charge enclosed by $S$, and $V$ is the volume enclosed by $S$.
\subsection{Definition (Differential form)}
In its differential form, Gauss's law is
\begin{displaymath}
\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}
\end{displaymath}
where $\nabla$ is the divergence operator, and $\rho$ is the charge density.
\subsection{Gauss's Law with Electric Displacement}
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