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

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

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.