Question

Explain displacement current?

Answer 1

Displacement current \(J_D\) is the rate of change of the displacement field \(D\) that exists in dielectric materials (of permittivity \(\varepsilon =\varepsilon_{r}\epsilon_{0}\)) , and is the product of the movement of bound charges from their equilibrium positions upon the application of an electric field.

When an electric field \(\bar{E}\) is applied across a dielectric material of susceptibility \(\chi\) it will induce a dipole moment such that \(\bar{p}=Q\bar{d}\) with the net dipole moment per unit volume being defined as the Polarisation \(\bar{P}\) where \[\bar{P}=\epsilon_{0}\chi\bar{E}\]where \(\epsilon_{0}\) is the permittivity of free space. However, since \(\chi=\varepsilon-1\) the Polarisation can then be equated to \[\bar{P}=(\varepsilon_{r}-1)\varepsilon_{0}\bar{E}\] where \(\varepsilon_{r}\) is the relative dielectric permittivity of the material (also known as the materials "dielectric constant"). We can now define the Displacement field \(\bar{D}\) as \[\bar{D}=\varepsilon_{0}\bar{E}+\bar{P} \] and hence the rate change with respect to time is \[\bar{J_D}=\frac{\partial\bar{D}}{\partial t}=\varepsilon_{0}\frac{\partial\bar{E}}{\partial t}+\frac{\partial\bar{P}}{\partial t}\]What this tells us that when one applies a field, the bound charges within a dielectric will be displaced with respect to their equilibrium values to produce a polarisation of the material that is proportional to the applied electric field (the constant of proportionality being the permittivity of the material. It is this displacement of charge (which produces the displacement field). However, as the bound charges are shifting from their equilibrium positions, the displacement field changes with time, and hence a displacement current is formed. One can think of this displacement current is a function of the normal electric current and the polarisation current. Looking at the above equation, one can see that for a constant applied electric field (i.e. an instantaneous applied DC field), all displacement current is from the polarisation of the dielectric, as the dipoles try to reorientate to the field. The attached diagram shows an approximation of how the polarisation in such a material behaves upon the application of and electric field.

Things get a lot more complicated when AC fields are in play.