A parallel plate capacitor is being charged by a time varrying current. Explain briefly how Ampere's circutal law is generalised to incorporate the effect due to the displacement current.

Explanation

While dealing with the charging of a parallel
plate capacitor with varrying current, it was found
that Ampere's circutal law is not logically
consistent, because `oint_CvecB.vec(dl)` has to same
value on the two sides of a plate of charged
capacitor. The incosistancy of Ampere's
circutal law was removed by Maxwell's by
predicting the presence of displacement current
in the region between the plates of capacitor,
when the charge on capacitor is changing with
time. Maxwell also predicted that the sum of
conduction current and displacement current has
the property of continuty.
The generalised from of Ampere's circutal law,
The generalised form a Ampere's circutal law,
modified by Maxwell states that
`oint vecB.vec(dl)=mu_0(I+I_D)=mu_0(I+in_0 (dphi_E)/(dt))`