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 Φ = q 1 + q 2 ε 0 {\displaystyle \Phi ={\frac {q_{1}+q_{2}}{\epsilon _{0}}}} \vspace{10 pt} \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 [ μ C ] {\displaystyle 10.5\,\,[\mu C]} and the charge on the cat 2 is 12.2 [ μ C ] {\displaystyle 12.2[\mu C]} , then the total flux through G {\displaystyle G} is Φ = 10.5 × 10 − 8 [ C ] + 12.2 × 10 − 8 [ C ] 8.85 × 10 − 12 [ C 2 / N m 2 ] {\displaystyle \Phi ={\frac {10.5\times 10^{-8}\,[C]+12.2\times 10^{-8}\,[C]}{8.85\times 10^{-12}\,[C^{2}/Nm^{2}]}}} Φ = 3073.4 [ N m 2 / C ] {\displaystyle \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. Figure 1, The Cat Clip art is public domain and was downloaded from [ http://www.wpclipart.com/ WP Clipart]
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