PlanetPhysics/A Cats Meow Application of Gauss Law

If you know the amount of charge contained within a Gaussian surface, then the total flux of the Electric Field generated by the enclosed charge is calculated from Gauss' Law.

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

$\Phi ={\frac {q_{1}+q_{2}}{\epsilon _{0}}}$

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

{\mathbf Figure 1:} Gaussian Surface Encompassing Two Cats

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

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

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.