State Ampere's circuital law.

Explanation

Maxwell argued that a changing electric field between the capacitor plates must induce a magnetic field.As currents are the usual sources of magnetic field must be associated with a current .Maxwell called this current as the displacement current. If .A. be the area of the capacitor plates and .q. be the charge on the plates at any instant .t. during the charging process,then the electric field in the gap will be
`E=(sigma)/(epsilon_0)=q/(epsilon_0+QA)(or)EA=q/(epsilon_0)`
Flux `Phi_E=q/(epsilon_0)`
`therefore (dPhi_E)/(dt)=d/(dt)((q)/(epsilon_0))=(1/(epsilon_0))((dq)/(dt))`
But `(dq)/(dt)` is the rate of change of charge on the capacitor plates.It is called displacement current and is given by `therefore (dPhi_E)/(dt)=d/(dt)((q)/(epsilon_0))=1/(epsilon_0))((dq)/(dt))`
This is the missing term in Amoere.s Law. The total current must be the sum of the conduction current `I_d` and the displacement current `I_d` thus, `I=I_c+I_d=I_c+epsilon_0 (dPhi_E)/(dt)`.
`oint overlineB.overline(dl)=mu_0(I_c+epsilon_0(dPhi_E)/(dt))`