Electric Displacement

Electric displacement is a term that appears in Maxwell’s equations of electromagnetism. It is a vector field and is denoted by ‘D’. Electric displacement was used by Maxwell to account for the discrepancy in Faraday’s equations on the same subject. Faraday couldn’t explain the effect due to bound charges in a capacitor. While the equation predicted accurately for charges that were in motion like in a conductor, it failed when it encountered a combination of both charges at rest and in motion. Maxwell resolved this discrepancy by introducing the concept of electric displacement, also called the electric displacement field.

It postulated that the displacement current is given by flux density for charges at rest due to the separated charges. This concept also helped in the understanding of Gauss’ law and reconciled it with other equations of electromagnetism. It is expressed in the SI unit of coulomb per unit square (C⋅m-2).

The electric displacement field is the result of the electric field due to all the free charges and all the dipoles in a system. This displacement field does not occur until some external potential polarises the system. When we apply an external potential to the ends of an insulating material, for example, as in a dielectric substance between the plates of a capacitor, then the field due to free charges that accumulate at either end of the material on the plates of the capacitor produces an electric field across the dielectric material. This field causes the bound charges in the material to separate a little.

This happens between the neutralised charges in atoms and molecules. When such a system has been formed, then the dielectric material is full of several dipole moments. These dipole moments produce a field of their own and contribute to the total electric displacement field in the system. The change of this displacement field gives the value of the displacement current that is passing between the plates of the capacitor. The electric displacement field can therefore be written as:

D = ε₀E + P

Here,

D is the electric displacement field

E is the electric field produced due to polarised free charges

P is the dipole moment density of the material

ε₀ is the absolute permittivity of vacuum

Note: Here, P is evaluated by taking into account both permanent and induced dipole moments in the system.

The electric displacement is a changing quantity. It changes with time. For charges that are fixed in magnitude, the displacement current is zero. Moreover, the change in the displacement field is only due to the free charges in any system. The change due to permanent and the induced dipoles cancels out due to cancellation of the magnitude of charges in a dipole. Therefore, free charges are solely responsible for the creation of polarisation in any system. That is why the flux of the field in the electric displacement must begin and end at free charges.

This is because the field due to dipoles is confined in a loop. The free charges in the system also go by the name of space charges. For a system of charged capacitor plates, the free charges reside on the surface of the plates, and the induced and permanent dipoles are present inside the dielectric material between the plates. Therefore, the total electric displacement can be accounted for by adding the fields due to the free charges on the plates as well as the dipole moments in the dielectric material. But the displacement current is only caused due to the change in the magnitude of charges on the capacitor plates. If the dielectric material is replaced by something that has free charges like a semiconductor or an ionised gas, then the free charge content of the system will rise, and the total free charge at the plates will be the sum of the charges induced on the plates and the free charges contributed by the material.

However, on an important note, it can be observed that in the case of materials like electrets, which are the electric equivalent of a bar magnet, the displacement field is decided exclusively by bound charges.

In an electret, the electric field is produced by the permanent polarisation of the material that causes an electric field to be generated by the dipole on the extremities of the material. There being no free charges in the system, the entirety of the electric displacement field is decided by the field due to the permanent dipole. Inducing a change in such a system is very difficult without the aid of external free charges.