What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell's law.
When a capacitor is charging (or discharging), current flows in the circuit. However, there is no actual charge transfer in the insulated region between capacitor which is contradictory to the flow of current. Hence, displacement current is the current in the insulated region due to the changing electric flux.
For a charged capacitor, electric field between the plates is given by:
E=QεoA
Q=εoϕE
Displacement current is given by:
id=dQdt=εodϕEdt
According to Maxwell's Ampere circuital Law, the line integral of magnetic field along a closed path is equal to μo times the total current.
∮→B.→dl=μo(ic+id)
where ic: Conduction current
id: Displacement current