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

(1)

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 [μC] and the charge on the cat 2 is 12.2[μC], then the total flux through G is

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.

References