We know, According to Ampere's Circuital law, the line integral of the magnetic field B along any closed loop C is proportional to current I passing through the closed loop.
In 1864 Clerk Maxwell showed that equation (1) is inconsistent. In order to prove this, he has given an example of a parallel plate capacitor which is being charged. As the capacitor is being charged so we can say that the charges on the plates of the capacitor is increasing and hence the electric field between the plates of the capacitor. In order words, the electric field between the plates are not constant but changing.
As you can see in the above figure, the current through the surfaces 1, 2 and 4 is I and so the line integral of the magnetic field will be µ₀I but the current through the surface 3 will be zero and hence the line integral of the magnetic field is also zero.
Hence, the Ampere's circuital law is not consistent everywhere. This is why Maxwell modified the Ampere's Circuital law.
Concept of Displacement Current
During the modification of Ampere's law, Maxwell applied the concept of symmetry. He explained that as per the Faraday's law of electromagnetic induction, changing magnetic field induces and electric field (voltage) so changing electric field must induce a magnetic field (current).
In other words, whenever there is a change in electric field or electric flux then there must be a current which is different from the normal current / conduction current / current which flow due to the flow of electrons. Maxwell named this current as displacement current.
Hence the modified Ampere's Circuital law looks like
where ID is displacement current.
Definition of Displacement Current
It is that current which is produced apart from the conduction whenever the electric field and hence the electric flux changes with time.
Hence, the modified Ampere's law could be written as
Properties of Displacement Current :
1) Displacement current only exist when there is a change in electric field. During the steady state, the displacement current will cease.
2) The magnitude of the displacement current is equal to the rate of displacement of charge from one plate of capacitor to the other.