Electric Flux

We define the Electric Flux as the rate of flow of the electric field through a given area and it varies directly with the number of electric field lines going via a virtual surface.

Switch on the mosquito repellent, you smell the fragrance after some time. So, here, lines (electric field lines) of fragrance passing through the area of the room are the electric flux. 

On this page, you will learn what is electric flux, electric flux definition in detail.

What Is Electric Flux?

In terms of electromagnetism, electric flux is the measure of the electric field lines crossing the surface. Although an electric field cannot flow by itself, it is a way of describing the electric field strength at any distance from the charge creating the field. The electric field E can generate a force on an electric charge at any point in space.

Concept of Electric Flux

In the above text, we understood the electric flux definition. Now, let’s understand the concept of electric flux.

Let’s consider a hypothetical (imaginary) planar element of area ΔS and a uniform electric field exists on the plane surface.

We know that the number of field lines crossing a unit area placed normal to the electric 

field E at a point is a measure of the strength of the electric field at that point.

Now, draw a line normal to the surface and call one side of it the positive normal to the surface.

If we place a smaller planar element of an area ΔS normal to \[\vec{E}\] at this point electric field lines crossing this area are proportional to EΔS.

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Point To Remember

Please note that it doesn’t mean that the number of field lines crossing this area is equal to E ΔS.

Flux of Electric Field

If we tilt the area element by an angle Ө (or we tilt/rotate \[\vec{E}\] with respect to the area element by an angle Ө, the number of electric field lines crossing the area will be smaller.

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As the projection of area element normal to \[\vec{E}\] is ΔS CosӨ (or the component of  \[\vec{E}\] normal to area element is  E CosӨ).

Therefore, the number of electric field lines crossing area ΔS  is proportional to the following components in the equation:

Unit of Electric Flux

Dimensional Formula of Electric Flux

What Is Flux In Electrical?

Let’s suppose that we draw a vector of the magnitude ΔS along with the positive normal. ΔS is called the area-vector. The equation for the electric flux through a given area is:

Where,

Φ =  Electric flux which is proportional to the number of field lines cutting the area element.                                                  

 Ө  is the smaller angle between \[\vec{E}\] and \[\vec{\Delta S}\].

Now, let’s look at the following cases to determine the electric flux at certain angles:                                         

1. When \[\vec{E}\] is normal to the area element times the magnitude of area element, 

Ө = 0°, Φ is maximum. (∵ Cos 0° =1)

2. When \[\vec{E}\] is along with the area element, Ө = 90°,  Φ is zero.

3. When  Ө >  90°, CosӨ is negative,i .e., Φ is negative.

Now, let’s solve a problem to understand the flux of electric field:

Question: Let’s Say that Charge q is Placed at the Centre of a Sphere. Taking Outward Normal as Positive. Determine the Flux of the Electric Field via the Surface of the Sphere Due to the Enclosed Charge.

Solution: Let us take a small element ΔS on the surface of the sphere 

(Figure.a). The electric field here is radially outward and has the following magnitude:

 = q /( 4 x π x 𝛆o x r²)

Here,

q is the charge inside the sphere 

r is the radius of the sphere

𝛆o is the permittivity of free space

As the positive normal is also outward,  Ө = 0° and flux via this element are given by:

Δ Φ = \[\vec{E}\] . \[\vec{\Delta S}\] = E ΔS Cos 0° = E ΔS

=> Δ Φ =  q / (4 x π x 𝛆o x r² x  ΔS)

Summing over all the elements of the spherical surface

Φ  = ∑  Δ Φ =   q / (4 x π x 𝛆o x r² ∑ ΔS)…(1)

The surface area of the sphere ΔS =  4 x π  x r²…..  putting this value in eq (1), we get:

=  q / (4 x π x 𝛆o x r² x 4 x π x r²)

This is the required equation for the electric flux enclosed in the sphere. It means that the electric flux equation remains the same.