Electric Flux | Electric Flux Density

We know that there is an electric field around a point charge, and whenever there is an electric field there is an electric flux around it, this field though theoretically assumed to be spread up to infinity but practically they are taken to be composed of small closed areas. But what is this field made of? Or what is the component of this electric field? The field is nothing but an energy field, i.e. to go through the field work is done by or done upon a point charge. So, there must be some kind of energy present in the electric field. Now from each point of this electric field tube force emerges, which radiates through the surrounding. Now this total number of force tube is called electric flux.

Electric Field Due to a Point Charge

Let a point charge Q get placed and an imaginary spherical surface of radius r is kept around it so that the point charge Q rests at the center of the sphere. Now the total number of flux radiating from the charge (Q Coulombs) is equal to Q coulombs. We can prove it also.

Now, the electric field intensity at any point on the surface is

Electric Field due to a Point Charge

Electric Field due to a Point Charge

The field intensity is normal to the surface of the sphere at that point.

Theoretically the number of electric flux crossing the sphere at that point is infinite but practically the flux at that point is εoεr times the intensity of the field. Which is equal to

Surface area of the sphere = 4πr2

→ the total number of flux radiating from the charge is Q

So, electric field due to a point charge is equal to the charge in coulombs.

Electric Flux Density

We have seen that the tube forces which are termed as electric flux, radiates normally from the surface and is assumed to be infinite in no. the amount of radiating this flux through unit surface area is known as electric flux density. The unit of this is coulombs/m2.

Let's take a point charge of Q coulomb and place it at the center of a sphere of radius ’r’ then the electric flux density is

From the above relation we can see that the electric flux density does not depend on the medium, i.e. the absolute permittivity and relative permittivity, and it is inversely proportional with the square of the distance from the charge.

The relation between electric flux intensity and density is given by the equation

Electric Dipole Moment

The most basic definition of an electric dipole moment can be given as the system consisting of two equal in magnitude but opposite charges separated by certain distance, it can be infinite or less than that. Let us assume two point charges +Q and –Q, both have same magnitude i.e. Q coulomb, but one of them has positive charge and the other one is negatively charged, now the dipole moment is the vector at the mid point between the two charges and denoted by P and represented as

P = Q.d

Where, Q is the charge and d is the distance between the two charges.

In a polarized material the molecules reside as electrical dipole. When that substance enters inside an electric field, the field causes the dipoles to orient parallel inside the substance. The net electric dipole moment of the substance at that point of time acts at the same direction and the sum of the dipole moments per unit volume in a material is called dielectric polarization.

Electric Displacement Vector

The electric field intensity is given by

We can see from the above equation that the intensity depends on the surrounding medium (here t which permittivity of the medium is different for various mediums), but there is another term electric displacement vector which only express the magnitude of the field and does not depend on the surrounding medium. It basically gives the amount of electric flux radiated normally through per unit surface area and it is unaltered by the change of medium. It is denoted by D and given as

The unit of electric displacement vector is coulombs/m2

From Gauss’s theorem the relationship between electric displace vector, electric field intensity and electric dipole moment E, D & P can be given by

D = εoE + P

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