1. Flux of the Electric Field
Electric flux is the rate of flow of the electric field through a given area
(Fig. 1). Electric flux is proportional to the number of electric field lines 
going through a virtual surface.
Figure 1: Electric Flux: Electric flux visualized. The ring shows the surface boundaries. 
The red arrows for the electric field lines.
Flat Surface, Uniform Field: We begin with a flat surface (Fig. 2) with area 
A in a uniform electric field �⃗ . The total flux  is then:
Φ = ∫ �⃗ . �� (����� ����)
Φ = ∫(� ����) �� (����� ����)
When the electric field is uniform and the surface is flat:
Φ = (� ����)� (uniform field, flat surface)
Figure 2: An electric field vector pierces a small square patch on a flat s