How does Ampere-Maxwell law explain the flow of current through a capacitor when it is being charged by a battery? Write the expression for the displacement current in terms of the rate of change of electric flux.

When battery is connected to a capacitor, current flows throughout

the circuit except between the plates of the capacitor. But, there

exists electric field between the plates which eventually create

magnetic field. It leads inconsistency in Ampere’s circuital law.

For this problem, concept of displacement current is

Introduced by Maxwell. He modifies the Ampere’s law as follows,

→ Ampere’s law

→ Ampere Maxwell’s law

Where, B = Magnetic field

I = current

I_d = displacement current

According to this law, displacement current is arise due to the changing electric field which in turn creates magnetic field between the plates.

Displacement current,

Where,

Φ_E = electric flux

ϵ₀ = permittivity of the space