Electrical Engineering ⇒ Topic : Electric flux density

Electric Flux Density (D)

The electric flux density at any section in an electric field is the electric flux crossing normally per unit area of that section i.e.

Electric flux density, D = Ψ /A

The SI unit of electric flux density is *C/m².

For example, when we say that electric flux density in an electric field is 4C/m², it means that 4C of electric flux passes normally through an area of 1m². Electric flux density is a vector quantity; possessing both magnitude and direction. Its direction is the same as the direction of electric intensity.

Relation between D and E. Consider a charge of +Q coulombs placed in a medium of relative permittivity 8, as shown in Fig. (a). The electric flux density at P at a distance d metres from the charge can be found as follows. With centre at the charge and radius d metres, an imaginary sphere can be considered. The electric flux of Q coulombs will pass normally through this imaginary sphere. Now area of sphere = 4Πd².

                                                      figure (a)

Hence flux density at any point in an electric field is ε₀ε_rtimes the electric intensity at that point.

The electric flux density (D) is also called electric displacement.It may be noted that D and E are vector quantities having magnitude and direction. Therefore,in vector form

The direction of D at every point is the same as that of E but its magnitude is D = ε₀ε_r,E.

The value of E depends upon the permittivity ε(= ε₀ε_r ) of the surrounding medium, that of D is independent of it.

Electric flux density (D) D = ε₀ε_r,E.is directly related to electric field intensity (E) ; permittivity ε(= ε₀ε_r ) of the medium being the factor by which one quantity differs from the other.

The importance of relation D = ε₀ε_r,E. lies in the fact that it relates density concept to intensity concept.

Electric intensity at a point is also defined as equal to the electric lines of force passing normally through a unit cross-sectional area at that point. If Q coulombs is the charge, then number of electric lines of force produced by it is Q/ε. If these lines fall normally on area Am² sun-ounding the point, then electric intensity E at the point is

Electric Flux Density (D)
Consider the electric flux line emanating from a positive charge q as shown in Fig. (a) . Consider a sphere of radius r centered around the charge. The electric flux lines are radial and therefore they are normal to the surface of the sphere.Total flux leaving the surface is q and the surface area of the sphere is 4πr². Then the electric flux density (D) is defined as the flux per unit area. Therefore, D on the surface of the sphere of radius r is

                                         FIGURE (a) Electric flux lines due to + q

                                                                 ................ (1)

                                               .............. (2)

However, from Eq.(1)  we know that the electric field intensity at the surface

From Eqs. (1) and (2) we have

                                                                       ............... (3)

The unit of electric flux density D is Coulombs/m².
The above equation is valid for free space. For any other medium whose permittivity is ε.

                                                                     .................. (4)

where ε= ε_o, ε_r = permittivity of the medium.