Question

What is displacement current? How is displacement current different from conduction current?

Hint:

Recall Maxwell's correction to Ampere's law: a changing electric flux acts as a current, \( I_d = \varepsilon_0\, d\Phi_E/dt \), unlike conduction current which is real charge flow.

Answer 1

Step 1: Meaning of displacement current.
Maxwell noticed that Ampere's circuital law is incomplete for a circuit that contains a capacitor. While the capacitor is charging, no charge actually crosses the gap between its plates, yet a magnetic field still exists there. Maxwell proposed that a changing electric field in the gap acts like a current. This current is called the displacement current.

Step 2: Formula.
If \( \Phi_E \) is the electric flux between the plates, the displacement current is
\[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \]
where \( \varepsilon_0 \) is the permittivity of free space. It is produced by a time varying electric field, not by the motion of charges.

Step 3: Conduction current.
The ordinary current \( I_c \) that flows in a wire due to the actual drift of free charges (electrons) is called the conduction current. Maxwell modified Ampere's law to
\[ \oint \vec{B}\cdot d\vec{l} = \mu_0\left(I_c + I_d\right) \]

Step 4: Key differences.
(i) Conduction current is due to the actual flow of charges; displacement current is due to a changing (time varying) electric field, with no real charge flow.
(ii) Conduction current flows through a conductor; displacement current can exist even in vacuum or in the gap of a capacitor.
(iii) Both produce a magnetic field and together keep the total current continuous around a circuit.

\[\boxed{I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}}\]