Displacement current
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Displacement current is a pseudocurrent invented in 1865 by James Clerk Maxwell when formulating what are today known as Maxwell's equations. It is defined by the flux of the electric field through the surface:
- <math> I_D =\epsilon \frac{d\Phi_E}{dt} <math>
It is incorporated into Ampère's law, whose original form works only for surfaces that are well-defined (continuous and existing) in terms of current. 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 charge is found in electric flux, the change in the electric field; and while displacement current is not a current of electric charge, it produces the same result of generating a magnetic field.
A displacement current can be thought of as an elastic response of a material to an applied electric field. As an applied electric field is increased, the displacement current is stored in the material, and when the electric field is decreased, the material releases the displacement current. A perfect dielectric is a material that shows displacement current only, storing and returning electrical energy as if it were an ideal 'battery'.
The corresponding current density can be found by setting <math>\Phi_E = EA<math> and using <math>J_D = I_D/A<math> to arrive at:
- <math> \mathbf{J}_D = \frac{\partial \mathbf{D}}{\partial t} =\epsilon \frac{\partial \mathbf{E}}{\partial t} <math>
Here, the expression in terms of the displacement field <math>\mathbf{D}<math> is more general, since the <math>\epsilon<math> form at right assumes that the dielectric constant is time-independent (not true in a general dispersive medium).