Displacement current

Displacement current is a changing electric field; it is not a real current (movement of charge), but it has the units of current, and creates a magnetic field, as current does. It was formulated in 1865 by James Clerk Maxwell when formulating what are today known as Maxwell's equations. The displacement current density is mathematically defined by the rate of change of the electric displacement field:

\mathbf {J} _{D}={\frac {\partial \mathbf {D} }{\partial t}}=\varepsilon {\frac {\partial \mathbf {E} }{\partial t}}

The scalar value of displacement current may also be expressed in terms of electric flux:

I_{D}=\varepsilon {\frac {d\Phi _{E}}{dt}}

(The forms in terms of $\varepsilon$ are only correct for linear isotropic materials, unless you consider $\varepsilon$ to be a tensor, in which case they are valid for all linear materials.)

Maxwell incorporated the displacement current term into Ampère's law, whose original form does not work for time-varying currents. A surface S₁ chosen to include only one plate of a capacitor should have the same current as a surface S₂ chosen to include both capacitor plates. However, because charge stops at the first plate, Ampère's Law concludes there is no charge enclosed by S₁. To compensate for this difference, Maxwell reasoned that Ampère's law needed an additional term, the displacement current term, to be consistent.

Kirchhoff's current law also requires displacement current to be included in order to be valid for time-varying currents; for example, it is required when applying that law to one of the plates of a capacitor.

Maxwell interpreted the displacement current as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. Although this interpretation has been abandoned, Maxwell's correction to Ampere's law remains valid (a changing electric field produces a magnetic field).

See also