Electric flux for closed surfaces
In the previous section, the electric flux for any arbitrary curved surface is discussed. Suppose a closed surface is present in the region of the non-uniform electric field as shown in Figure 1.35 (a).
The total electric flux over this closed surface is written as
Note the difference between equations (1.57) and (1.58).
The integration in equation (1.58) is a closed surface integration and for each areal element, the outward normal is the direction of as shown in the Figure 1.35(b).
The total electric flux over a closed surface c1an be negative, positive or zero. In the Figure 1.35(b), it is shown that in one area element, the angle between d and is less than 90º, then the electric flux is positive and in another areal element, the angle between d and is greater than 90º, then the electric flux is negative.
In general, the electric
flux is negative if the electric field lines enter the closed surface and
positive if the electric field lines leave the closed surface.