Displacement Current — Definition

Definition

Imagine you're charging a capacitor. As charge flows onto one plate and away from the other, there's a current in the wires connecting to the capacitor. This is a 'conduction current' – a flow of actual charge carriers (electrons).

But what happens in the gap between the capacitor plates, where there's no physical connection and no charge carriers can move across? Ampere's original circuital law, which relates magnetic fields to electric currents, seemed to suggest that a magnetic field should only exist where there's a conduction current.

However, experiments showed that a magnetic field *does* exist in the space between the capacitor plates, even though no charge is physically flowing across the gap. This was a major puzzle.

James Clerk Maxwell, a brilliant physicist, realized that Ampere's law was incomplete when dealing with situations where electric fields change over time. He proposed a revolutionary idea: that a changing electric field itself could act as a source of a magnetic field, just like a moving charge (conduction current) does.

He called this equivalent current the 'displacement current'. It's crucial to understand that displacement current is *not* a flow of electrons or any other charge carriers. Instead, it's a conceptual current, a mathematical construct that represents the effect of a time-varying electric field.

Think of it as a 'displacement' of electric lines of force, or more accurately, the rate at which electric flux is changing through a surface.

In the charging capacitor example, as the capacitor charges, the electric field between its plates increases. This increasing electric field means the electric flux through the area between the plates is changing.

Maxwell's displacement current accounts for this changing electric flux, effectively 'filling the gap' in Ampere's law. By adding the displacement current term, Ampere's law became the Ampere-Maxwell law, which is one of the four fundamental Maxwell's equations.

This corrected law not only explained the magnetic field in the capacitor gap but also predicted the existence of electromagnetic waves, which travel through space even in the absence of any charge carriers.

Thus, displacement current is a cornerstone of electromagnetic theory, essential for understanding how light and other electromagnetic waves propagate.