Displacement Current - Explanation

Explanation

The electric displacement field is defined as:

where:

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:

The first term on the right hand side is present in material media and in free space. It doesn't necessarily involve any actual movement of charge, but it does have an associated magnetic field, just as does a current due to charge motion. Some authors apply the name displacement current to only this contribution.

The second term on the right hand side is associated with the polarization of the individual molecules of the dielectric material. Polarization results when the charges in molecules move a little under the influence of an applied electric field. 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.

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 ε_r in the relation D = ε_rε₀ E.

The modern justification of displacement current is explained below.