30.10 : Significance of Displacement Current

Displacement current is defined in terms of a time-varying electric field and has an associated displacement current density.

To understand the significance, consider a circular-shaped parallel capacitor.

A conduction current flows throughout the wires, but there is no conduction current in the region between the capacitor plates as there is no charge flow.

If a compass needle is placed between the capacitor plates, deflection is observed, confirming the presence of a magnetic field.

Displacement current accounts for this continuity of magnetic field in the region between the capacitor plates.

Applying generalized Ampere's law to find the magnetic field between the plates. 

For this, consider an Amperian loop with a radius less than that of the capacitor.

The line integral of the magnetic field along this loop equals the magnetic field times the circumference.

The current enclosed by the loop equals the product of current density and the enclosed area.

Thus, the magnetic field between the plates of the capacitor is obtained, which is zero at the axis and increases linearly with increasing distance from the axis.