Question

Considering the case of a parallel plate capacitor being charged, show how one is required to generalize Ampere's circuital law to include the term due to displacement current.

Answer 1

Using Gauss’ law, the electric flux ΦE of a parallel plate capacitor having an area A, and a total charge Q is Where electric field is As the charge Q on the capacitor plates changes with time, so current is given by i = dQ/dt This is the missing term in Ampere’s circuital law. So the total current through the conductor is
i = Conduction current (ic) + Displacement current (id) As Ampere’s circuital law is given by After modification we have Ampere−Maxwell law is given as The total current passing through any surface, of which the closed loop is the perimeter, is the sum of the conduction and displacement current.

Answer 2

Answer:

The space between the capacitor consists of an insulator. Hence, no actual transfer of charge occurs in this region. Current flows in the circuit during the charging of a capacitor. This demands the need of the presence of a displacement current in the capacitor resulting in a magnetic field.

∫B.dl=μo I

Here I is the sum of conduction and displacement currents.