Gauss Law states that "the total electric flux (ΔΦ) through a closed surface is equal to 1/ε₀ times the total charge contained within it, and does not depend on the location of the charge(s) within the closed surface. Put in another way, the total of the electric flux out of a closed surface is equal to the charge enclosed, divided by the permittivity, as shown in the Figure 5 below:

Figure 5

ΔΦ = E ΔA ………………………… (2-9)

The integral form of Gauss Law is the area integral of the electric field over any closed surface equal to the net charge enclosed in the surface divided by the permittivity of the vacuum (ε _o), as shown in the Figure 6 below.

Figure 6

Gauss Law is a very good way for the calculation of symmetrical electric fields as below shown in Figure 7.

Figure 7