30.6: Displacement Current
Ampère's law, in its usual form, does not work in places where the current changes with time and is not steady. Thus, Maxwell suggested including an additional contribution, called the displacement current, Id, to the real conduction current I.
where the displacement current is defined to be
Here, ε0 is the permittivity of free space, and ΦE is the electric flux.
The displacement current is an extra term in Maxwell's equations that is analogous to a real current in Ampère's law. However, it is produced by a changing electric field. It accounts for a changing electric field producing a magnetic field, just as a real current does, but the displacement current can produce a magnetic field even when no real current is present. When this extra term is included, the modified Ampère's law equation becomes
In this way, Ampère's law can be modified so that it works in all situations, and it is independent of the surface through which the current I is measured.