Question

Explain the inconsistency of Ampere's circuital law during charging of a capacitor. Define displacement current.

Answer 1

In classical electromagnetism, Ampere's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.

Ampere's law is valid only when there is a steady flow of current or electrostatic flux through a closed surface remains conserved, but at time of charging or discharging the flux does not remain conserved or there is no steady state.

So ampere law fails there, when displacement current is also considered then the flux remains conserved or we get steady state condition.

(i) The conduction and displacement currents are individually discontinuous, but the currents together possess the property of continuity through any closed electric circuit.

(ii) The displacement current is precisely equal to the

conduction current when the two present in different parts of the circuit.

(iii) The displacement current arises due to the rate of change of electric flux (or electric field) between the two plates of the capacitor.

(iv) Just as the conduction current, the displacement current is also the source of magnetic field.