30.10: Significance of Displacement Current

A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.

The presence of displacement current in the region between the plates of a charging capacitor accounts for the continuity of the magnetic field, which can be observed by placing a compass needle in the region between the capacitor plates. The generalized Ampère's law can be applied to obtain the magnetic field in the region between the plates of a charging capacitor, where no conduction current is present due to the absence of charge flow.

The magnetic field between the plates of the capacitor is found to be zero at the axis and increases linearly with increasing the distance from the axis.

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.