**What is Electric Flux?**

In this section, we will discuss the concept of electric flux, its calculation, and the analogy between the flux of an electric field and that of water. Let us imagine the flow of water with a velocity *v *in a pipe in a fixed direction, say to the right. If we take the cross-sectional plane of the pipe and consider a small unit area given by *ds* from that plane, the volumetric flow of the liquid crossing that plane normal to the flow can be given as *vds*. When the plane is not normal to the flow of the fluid but is inclined at an angle *θ*, the total volume of liquid crossing the plane per unit time is given as *vds*.cos*θ*. Here, *ds*cos*θ *is the projected area in the plane perpendicular to the flow of the liquid.

Consider a plane surface of area ΔS in a uniform electric field E in the space. Draw a positive normal to the surface and θ be the angle between electric field E and the normal to the plane.

Electric flux of the electric field through the chosen surface is then

Corresponding to area ΔS we can define area vector ΔS of magnitude ΔS along the positive normal. With this definition one can write electric flux under the direction of area vector is always along normal to the surface being chosen.

Thus electric flux is a measure of lines of force passing through the surface held in the electric field.

**Special Cases:**

- If E is perpendicular to the surface i.e., parallel to the area vector then θ = 0.

- If θ = π i.e., electric field vector is in the direction opposite to area vector then

- If electric field and area vector are perpendicular to each other then θ = π/2 and ∆ϕ = 0.
- Flux is a scalar quantity and it can be added using rules of scalar addition.
**The unit of electric flux is NC**^{-1}m^{2}.