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Displacement current

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do. However it is not an electric current of moving charges, but a time-varying electric field. In materials, there is also a contribution from the slight motion of charges bound in atoms, dielectric polarization.
The idea was conceived by James Clerk Maxwell in his 1861 paper (On Physical Lines of Force, Part III ) in connection with the displacement of electric particles in a dielectric medium. Maxwell added displacement current to the electric current term in Ampère's Circuital Law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this amended version of Ampère's Circuital Law to derive the electromagnetic wave equation. This derivation is now generally accepted as a historical landmark in physics by virtue of uniting electricity, magnetism and optics into one single unified theory. The displacement current term is now seen as a crucial addition that completed Maxwell's equations and is necessary to explain many phenomena, most particularly the existence of electromagnetic waves.
== Explanation ==

The electric displacement field is defined as:
:$\boldsymbol = \varepsilon_0 \boldsymbol + \boldsymbol\ .$
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:
:$\boldsymbol_ \boldsymbol = \varepsilon_0 \frac + \frac\ .$
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 does a current due to charge motion. Some authors apply the name ''displacement current'' to the first term by itself.〔For example, see and 〕
The second term on the right hand side 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.
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.

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