Electric flux – definition, formula – In this post, we will define electric flux and study its equation. We will also study a few figures that come with numerical problems related to electric flux. Later, we will find the statement of Gauss’ theorem.

**Electric Flux** – definition

**Definition of flux:** The total number of electric field lines crossing a surface normally is called electric flux.

Electric flux can also be defined as the surface integral of the Electric Field over the entire closed surface.

**Electric Flux** equation | formula of electric flux

Formula or equation of electric flux: The electric field through surface element d**S** is ΔΦ = **E**.d**S = ***E dS cos θ*, where **E** is the electric field strength. (see figure 1)

The surface integral form of the flux formula is this: Φ_{E} = ʃ_{A} **E**. d**s**

This can be expanded as Φ_{E} = ʃ_{A} **E**. d**s** = ʃ_{A} **E** d**s** *cos θ* = ES *cos θ*

When, *θ* = 0° i.e., when the area vector and the electric field vector are parallel, then Φ_{E} = ES

Here, S = surface area.

[ Note: The area vector is normal (perpendicular) to the surface]

*θ* in the electric flux equation

*θ* is the angle between the direction of the Electric field **E** and the normal to the surface being considered.

In other words, *θ* is the angle between the direction of the Electric field **E** and the area vector.

[ Note: The area vector is normal (perpendicular) to the surface]

### How to quickly find this *θ* from a given figure or diagram when solving numerical problems?

θ = the minimum angle by which we have to rotate the **surface** plane to make it normal to **E** field line direction= minimum angle by which we have to rotate the **E** field line direction to make it normal to the Surface.

We will do this quick check because the definition of flux considers only the electric field lines crossing a surface normally. [normal means perpendicular]

## finding flux from figures

See figure 2.

### flux **In figure 2 (i):**

*θ* = angle between the direction of the Electric field **E** and the normal to the surface being considered = 0°.

In other words, the minimum angle by which we have to rotate the **E** field line direction to make it normal to Surface = 0°.

Hence, flux Φ = **E** **.** **A **= EA cos 0° = EA

### flux **In figure 2 (ii):**

*θ* = angle between the direction of the Electric field **E** and the normal to the surface being considered.

In other words, minimum angle by which we have to rotate the **E** field line direction to make it normal to Surface = *θ*

Hence, flux Φ = **E** **.** **A **= EA cos *θ*

### flux **In figure 2 (iii):**

*θ* = angle between the direction of the Electric field **E** and the normal to the surface being considered = 90°.

In other words, minimum angle by which we have to rotate the **E** field line direction to make it normal to Surface = 90°.

Hence, flux Φ = **E** **.** **A **= EA cos 90° = EA

**Gauss’s Theorem** statement

It states that the total electric flux through a closed surface is equal to **1/ε**_{0} times the net charge enclosed by the surface.

**Also read: Derivation of Gauss’ Theorem **