Displacement Current

Ampere's law states that the line integral of a magnetic field along a closed curve equals the permeability of free space times the net current passing through the loop.

Consider a parallel plate capacitor connected with a battery in a charging condition.

Applying Ampere's law to the shown Amperian loop with two surfaces gives two different magnetic field values, which is impossible.

As the capacitor is charging, the electric field, and hence the electric flux, increases through the bulging surface. The value of electric flux can be obtained in terms of the charge.

In 1865, James Clerk Maxwell, predicted that due to this time-varying electric field, a non-zero magnetic field is produced between the plates of the capacitor through a fictitious current called displacement current.

The expression for displacement current is given in terms of electric flux.

Thus, Ampere's law is modified with the inclusion of an additional term for displacement current. It is known as the Ampere-Maxwell law or generalized Ampere's law.