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Displacement Current

Maxwell introduced the new concept of displacement current. Faraday discovered that a changing magnetic field produces an electric field. Maxwell pointed out that a changing electric field produces a magnetic field.

Consider the plates of a parallel plate capacitor connected to the terminals of a battery. The conduction current from the battery gradually charges the capacitor plates. Until the voltages across the capacitor becomes equal to the battery voltage, conduction current flows in the leads of the capacitor. But the conduction current is not continuous across the gap between the plates as there is no transfer of charge across the plates. But according to Maxwell, the changing electric field between the plates serves the purpose of conduction current inside the gap. The displacement current in the gap is found to be equal to the condition current in the lead wires. This proves that the flow of current in a circuit is continuous. 

Magnitude of Displacement Current
Consider a parallel plate capacitor with free space between the plates. Let q be the charge given to one of the plates at any instant and A its area.

Electric field between the plates} = E = q/ε0A

    D = q/ ε0A x ε0 = q/A
Displacement current = id=AJd =A ∂D/∂t=A ∂/∂t (q/A)= (∂q/∂t)=i

Here ∂q/∂t is the current flowing in the circuit at that instant.
    . :    id = i

Hence the displacement current in the gap between the capacitor plates is equal to the conduction current in the lead wires. Thus the displacement current provides a continuous path for the charges across the capacitor.

Displacement Current

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