an application of Gauss' law a cat's meow

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

$\displaystyle \Phi = \frac{q_1 + q_2}{\epsilon_0}$ (1)



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

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

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

$\displaystyle \Phi = 3073.4    [N m^2/C]$

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.

Bibliography

1
Figure 1, The Cat Clip art is public domain and was downloaded from WP Clipart



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As of this snapshot date, this entry was owned by bloftin.