What is Electric Flux? Introduction, Properties, and Formula

Introduction to Electric Flux

Electric Flux can be defined as the number of electric field lines, passing through per unit area. It is a physical quantity used to measure the strength of the electric field.

Image 1: Electric flux passing through a plane surface

Before discussing the electric flux lets recall some important concepts related to it. First comes Electric Field (E), which is defined as the force per unit charge at a particular point.

E = F / q

Consider a point charge Q, and the electric field (E) on a test charge q due to this point charge at a distance r is given by the following equation.

where k is a constant with a value of 8.99 x 109 N m2/C2

Here a unit test charge ‘q’ is placed near a point charge ‘Q’ experiences a force due to its electric field. The direction of this force is represented by lines that are outward or coming out of a positive charge or going inwards to negative charge. These lines of force are called electric field Lines or Flux Lines.

Electric field lines

Properties of Electric Flux Lines

Flux lines are the lines of forces around a charge with the following given properties:

• Flux lines always originate at positive charges and terminate at a negative charge.

• The strength of any electric field depends on the number of flux lines. All the flux lines are parallel to each other in a particular field. The flux lines always enter or leave a charged surface.

The direction of electric flux lines

Now comes to Electric Flux

An Electric Field is imagined to be present around a charged particle, and that can be presented in terms of ElectricFlux. The field lines or flux lines can be used to pictorially present the distribution of Electric Flux around a charged particle.

• Representation Symbol of Electric Flux is Φ.

Electric Flux equation

Flux concept is always related to something called an electric field, passing through a given area. Then, these electric lines of flux passing through a given surface with a given area are dependent on the following:

• Electric Field strength

• Surface area

• Surface Orientation with respect to the lines of force

To understand the third point, consider a surface, which is injected through an electric field in three different orientations.

Surface Orientation with flux lines

Surface Orientation with flux lines

First, when a given surface is perpendicular to the electric field, a maximum number of flux lines are intercepted by the surface. Second, If the surface is parallel to the electric field, the number of field lines going through the surface is zero. But when the surface is put at the orientation angle θ, then the number of flux lines passing through the surface will be proportional to this angle.

Surface Orientation with flux lines

Generally, if the θ is represented the angle between the electric field vector and surface vector of the given surface, with area A, the number of flux lines passing through this surface is directly proportional to Cos θ.

ΦE αCos θ

On removing the proportionality sine we get

ΦE = E.A.Cos θ

Where, E is Electric Field with units newtons per coulomb (N/C) or volts per meter (V/m).

A is a surface area with units meter2

θ is the angle with units degrees or radians

Therefore, the units of Electric Flux are Newton meter2 / Coulomb (Nm2/C).

This formula is suitable if the surface has a deterministic area.

For the curved surface, the given area is divided into small parts of the area symbolize as‘d’ and the integration of the flux is taken over the entire surface.

ΦE = ∫E  .dA

A Real-Life Flux Capacitor

Capacitors are the energy storing devices, and these are very much use full in the electronics world. Whereas Flux is the amount of something moving across a particular area. So in a flux capacitor, microwaves are something, and the channel across they are moving is a central capacitor. The device forces microwaves signals to flow in only one direction around a central area, just like traffic moving in a one-way circular path as shown in the figure.

In future flux, capacitor devices will help researchers to precise control signals that are necessary for advance quantum computing. It could also help us improve the electronics we are using nowadays.

Dewakar Pandey
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