Electric Flux Density

Electric Flux Density (  )

• Consider the two point charges as shown in the Fig. 3.3.1 The flux lines originating from positive charge and terminating at negative charge are shown in the form of tubes.

• Consider a unit surface area as shown in the Fig. 3.3.1 The number of flux lines are passing through this surface area.

• The net flux passing normal through the unit surface area is called the electric flux density. It is denoted as   . It has a specific direction which is normal to the surface area under consideration hence it is a vector field.

• Consider a sphere with a charge Q placed at its centre. There are no other charges present around. The total flux distributes radially around the charge is ψ = Q. This flux distributes uniformly over the surface of the sphere.

Now, ψ = Total flux

While, S = Total surface area of sphere

then electric flux density is defined as,

D = ψ / S in magnitude ….. (3.3.1)

• As ψ is measured in coulombs and S in square metres, the units of D are C/m². This is also called displacement flux density or displacement density.

1. Vector Form of Electric Flux Density

• Consider the flux distribution, due to a certain charge in the free space as shown in the Fig. 3.3.2.

• Consider the differential surface area dS at point P. The flux crossing through this differential area is d ψ. The direction of    is same as that of direction of flux lines at that point. The differential area and flux lines are at right angles to each other at point P. Hence the direction of    is also normal to the surface area, in the direction of unit vector    which is normal to the surface area dS. Near point P, all the lines of flux d ψ are having direction of that of    as the differential area dS is very small. Hence the flux density    at the point P can be represented in the vector form as,

where  d ψ = Total flux lines crossing normal through the differential area dS

dS = Differential surface area

 = Unit vector in the direction normal to the differential surface area

Review Question

1. Explain the concept of electric flux density.