Talk:PlanetPhysics/A Cats Meow Application of Gauss Law

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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: an application of Gauss' law a cat's meow %%% Primary Category Code: 40-XX %%% Filename: ACatsMeowApplicationOfGaussLaw.tex %%% Version: 4 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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If you know the amount of \htmladdnormallink{charge}{http://planetphysics.us/encyclopedia/Charge.html} contained within a Gaussian surface, then the total \htmladdnormallink{flux}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} of the \htmladdnormallink{Electric Field}{http://planetphysics.us/encyclopedia/ElectricField.html} generated by the enclosed charge is calculated from \htmladdnormallink{Gauss' Law}{http://planetphysics.us/encyclopedia/GausssLaw.html}.

As a demonstration, imagine a pair of cats that have charges placed on them by their loyal masters. Although the contours of the cats' elegant frames represent a complicated geometry, calculating the flux is a simple task if the charge on the cats is known. The flux through the Gaussian surface in Figure 1 is given by Gauss' law

\begin{equation} \Phi = \frac{q_1 + q_2}{\epsilon_0} \end{equation}

\vspace{10 pt}

\begin{center} \includegraphics[scale=.6]{Cats.eps}

{\bf Figure 1:} Gaussian Surface Encompassing Two Cats \end{center}

Note that we add the charges in equation (1) because it is the net enclosed charge. For example if the charge on cat 1 is $10.5 \,\, [\mu C]$ and the charge on the cat 2 is $12.2 [\mu C]$, then the total flux through $G$ is

$$\Phi = \frac{10.5\times 10^{-8} \, [C] + 12.2\times 10^{-8} \, [C] }{8.85 \times 10^{-12} \, [C^2/N m^2]}$$ $$ \Phi = 3073.4 \,\, [N m^2/C]$$

The reverse of this problem is another important result. If we measure the flux through a given Gaussian surface, then we can calculate the amount of enclosed charge.

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\bibitem{Figure1} Figure 1, The Cat Clip art is public domain and was downloaded from \htmladdnormallink{WP Clipart}{ http://www.wpclipart.com/}

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