capacitor current and current lead concept

[Rajnaveen]

how does current flow through a capacitor when there is dia electric material in between positive and negative plate,
and why does current lead in capacitor with respect to voltage when there is a little flow of current?

 

[jiripolivka]

Try read the history of Maxwell equations. He introduced the displacement current, the flow of a charge through a capacitor.
Why the capacitor current "leads" is that a discharged capacitor behaves as a short to an incoming charge. In inductors to the contrary the current "lags" as it must first generate the magnetic field.