Electric Displacement Current has a curious history and meaning.

If we connect an AC voltage to a simple circuit with a capacitor, a sinusoidally varying Magnetic field appears around the wire. That is Ampere's Law.

What is odd is that an identical magnetic field seems to appear even in the gap between the plates of the capacitor identical to the magnetic field around the wire. This is most strange because no current ought to be flowing through the gap.

Maxwell boldly modified Ampere’s Law and introduced a current expressed in terms of a vector D, which he felt simply has to exist in empty space. This however, put him in a bit of a fix.

Currents in a conductor were understandable since free electrons were known to be the prime carriers of current. But what on earth could be the carriers of current in empty space?

Maxwell fudged. He dug out and dusted a theory that had been used to explain away how dielectrics between the plates increased capacitance. The electrical field across the capacitor’s plates was said to pull apart positive and negative charges (electron-proton pairs inside the dielectric) just a wee bit (like stretching a zillion little rubber bands) and realign their directions, such that these electron pairs effectively set up a electric counter-field in the opposite direction.

This minuscule movement of atomic particles inside a non-conductor under the influence of an electric field was referred to as ‘displacement’, where [math]D[/math] = [math]\epsilon{E}[/math] usually referred to as Electrical Flux density, from Gauss' Law and having the unit of measurement of [math]Coulomb/meter^2[/math]. This term ‘displacement’ came in as a handy explanation for that phantom current which Maxwell needed to clean up his equations.

Maxwell had tied himself into knots. Ok, so a conventional insulator could be said to have an electron-proton elastic stretch, but what about vacuum-based capacitors? Maxwell took recourse to the ‘Aether’ theory. The aether was supposed to be an all-pervading universal fluid that even filled vacuum .

Now we know better. There is no such stuff as the Aether, and vacuum does not have any electrons or protons that can get pulled apart.

However, Maxwell’s Equations were destined for a serendipitous happy ending.

Whereas that ‘displacement current’ seems to be fictitious stuff, it couldn’t be denied that a magnetic field does appear between the plates even in a vacuum capacitor, strongly indicative of either a deemed or an actual current.

Finally, of course, the cause of this magnetic field was traced to the change in the electric field across the plates, and an imaginary current would explain that magnetic field that mysteriously arose in that gap even though no charged particles flowed across it. What is uncanny about this fictitious current is that it creates exactly the same magnitude and pattern of magnetic field in the inter-plate gap, as is created by the conduction current around the wires leading to the capacitor! The current in the wires and the ghost current in the gap are, therefore, equal to one another, and seem to form a continuum, like in a series circuit! If it looks like a duck, quacks like a duck, it must be a duck!

It is this ghost current, and the magnetic field that it gives rise to, that lets us complete that satisfyingly symmetrical Yin & Yang interplay in EM field theory: A change in Magnetic Field sets up an Electric Field, and a change in Electric Field sets up a Magnetic Field.

To summarize then, the strict meaning of the term ‘Displacement’ is the small bit of yield that takes place in electron-proton pairs in non-conductors when they are placed in an electric field E. In the case of air or a vacuum, Displacement turns out to be mathematically the same as flux density.

This pulling apart of electron-proton pairs inside the non-conductor sets up an electric field D of its own, which is in a direction opposite to that of external electric field E that caused the displacement. The magnitude of this counter-field is proportional to the permittivity of the non-conductor.

This phenomenon also lends its name to Maxwell’s current of convenience in a round about way. Consider a simple electrical circuit with an EMF source of V volts connected to a parallel plate vacuum Capacitor. The application of this EMF transfers some charge Q from one plate to the other such that Q = [math]\epsilon_o\frac{VA}{d}[/math] where A is the area of the plates and d the interplate gap.

An electrical field gets set up between the plates where E=V/d, so we get Q=[math]\epsilon_o{EA}[/math].

Differentiating both sides w.r.t. time gives us current on the LHS.

[math]\frac{\partial{Q}}{\partial{t}}= [/math]Current I=[math]A\epsilon_o\frac{\partial{E}}{\partial{t}}[/math]

Dividing a Current by the area of cross-section of the conductor should give us a Current Density. Let us divide the two sides by Area A and see what happens.

Wow!! The RHS is simply the rate of change of an Electric Field with [math]\epsilon_o[/math] as a proportionality constant. Dividing the rate of change of Electric Field Intensity by A has given us a Current density, which has exactly the same unit of measurement as a real electron current density.

All Maxwell had to do was to equate this [math]\epsilon{E}[/math] to [math]D[/math] and call it Displacement Field Strength .

[math]\epsilon_o\frac{\partial{E}}{\partial{t}}[/math] =[math]\frac{\partial{D}}{\partial{t}}[/math] [math]=[/math] [math]Current[/math] [math]Density.[/math]

let us make a quick recap of Ampere’s Law as it applies to currents in a conductor. The Differential form of this law says:-

[math]\nabla[/math] x [math]B[/math] = [math]\mu_o{J}[/math] where J is the Current Density in the conductor and B is the magnetic Field around the conductor.

If we turn our attention to the space between the plates of a vacuum capacitor, we would be right in saying that :-

[math]\nabla[/math] x [math]B[/math] = [math]\mu_o\frac{\partial{D}}{\partial{t}}[/math] where D is the Flux Density [math]\epsilon_o{E}[/math] in the inter-plate gap of the capacitor.

With some careful bit of contemplation, we can extend this logic to open space without recourse to conductors or capacitors, and arrive at an explanation for the travel of an Electromagnetic wave through free space. Look at how [math]\mu_o\epsilon_o[/math] creeps into Ampere’s Law. [math]\mu_o\epsilon_o[/math] you may recall is equal to [math]\frac{1}{c^2}[/math] where [math]c[/math] is the speed of light in vacuum.

This Displacement Current then is no piece of fiction. Call it a pseudo-current if you wish. It flows like the mythical river Saraswati. It seems to truly flow in free space and between the plates of a capacitor, and is a genuine source of a magnetic field just like an actual current.

It is not an electric current of moving charges, but a consequence of a time-variation in an electric field.