Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current.
Given: -
The capacitor is charging with the current I,
The Ampere’s circuital law is,
Also, the flux of electric field through the capacitor plates is,
As the charge on the capacitor plates is changing with time there will be a current i, given as,
Using the equation (a), we can write i as,
So, other than the charging current Ic, the other current i, which is appearing due to the change in the charge on the capacitor plates is the missing term in the ampere’s circuital law which is known as displacement current, so the modified the Ampere’s circuital law an be written as,
Substituting the value of i, we get,
Where, 
is the magnetic field, 
is the length element, 
is the permeability of air 
is the permittivity of air, 
is the flux and IC is the conduction current (charging current). The above modified form of Ampere’s circuital law is known as the Ampere Maxwell’s law.
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