The electric displacement field is defined as:
- ε0 is the permittivity of free space
- E is the electric field intensity
- P is the polarization of the medium
Differentiating this equation with respect to time defines the displacement current density, which therefore has two components in a dielectric:(see also the "displacement current" section of the article "current density")
The first term on the right hand side is present in material media and in free space. It doesn't necessarily come from any actual movement of charge, but it does have an associated magnetic field, just as a current does due to charge motion. Some authors apply the name displacement current to the first term by itself.
The second term on the right hand side, called polarization current density, comes from the change in polarization of the individual molecules of the dielectric material. Polarization results when, under the influence of an applied electric field, the charges in molecules have moved from a position of exact cancellation. The positive and negative charges in molecules separate, causing an increase in the state of polarization P. A changing state of polarization corresponds to charge movement and so is equivalent to a current, hence the term "polarization current".
This polarization is the displacement current as it was originally conceived by Maxwell. Maxwell made no special treatment of the vacuum, treating it as a material medium. For Maxwell, the effect of P was simply to change the relative permittivity εr in the relation D = εrε0 E.
The modern justification of displacement current is explained below.
Isotropic dielectric case
In the case of a very simple dielectric material the constitutive relation holds:
where the permittivity ε = ε0 εr,
In this equation the use of ε accounts for
the polarization of the dielectric.
The scalar value of displacement current may also be expressed in terms of electric flux:
The forms in terms of ε are correct only for linear isotropic materials. More generally ε may be replaced by a tensor, may depend upon the electric field itself, and may exhibit frequency dependence (dispersion).
For a linear isotropic dielectric, the polarization P is given by:
where χe is known as the electric susceptibility of the dielectric. Note that: