# Displacement Current

The idea of displacement current originated from the study of the discharge of a capacitor.

Maxwell asserted that since all electric currents are closed, in the discharge of capacitor, the

conduction current is closed by a current known as displacement current( arising due to charge

in electric displacement in the dielectric) flowing in the dielectric between the capacitor plates.

Let us consider a parallel plate charged capacitor joined together by a conducting wire. The discharge current ‘i’flowing through the wire is equal to the rate of charge on

where E = electric field between the plates, A = area of each plate, d = distance between the

plates, ε0 = absolute permittivity of free space.

Therefore from equations (1) and (2), we have

Hence, at can be interpreted as a density of some current which completes the  discharge current. Thus, there is a displacement current density denoted by Jd = at

(measured by A/m2) entering the dotted volume (in Figure 7.28) in the region of capacitorplates. The displacement current cannot be detected directly, but its existence is confirmedby electromagnetic theory of light.

Significance of displacement current

• Displacement current is entirely different from conduction current, Displacement current is a current only in the sense that it produces a magnetic field in the empty space since the conduction current is zero.
• The magnitude of displacement current is equal to the time rate of change of electric displacement vector D. When the field does not vary with time, the displacement current is zero.
• Displacement current serves to make the total current continuous across discontinuities in the conduction current.
• The time varying electric field generates a time varying magnetic field because of the term-.

The term  does not change the fact that the magnetic fields are continuous