Displacement Current: Concept and Formula

• Normal electric current (Conduction Current) is the actual physical flow of electrons through a wire.
• However, inside a capacitor, there is a gap with empty space (or a dielectric) between the two plates. No electrons actually flow across this empty gap.
• Yet, a magnetic field still exists in that empty gap! Maxwell proposed that a changing electric field between the plates acts exactly like a real current, producing a magnetic field. He named this invisible 'fake' current the Displacement Current ($I_d$).

The formula for Displacement Current is: $I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$

Where:

• $I_d$ = Displacement Current
• $\varepsilon_0$ = Permittivity of free space ($8.85 \times 10^{-12} F/m$)
• $\Phi_E$ = Electric Flux
• $\frac{d\Phi_E}{dt}$ = The rate of change of electric flux with respect to time.

Maxwell updated Ampere's Circuital Law to include both the real wire current ($I_c$) and the gap current ($I_d$). The modified equation states that the total magnetic field is produced by the sum of both: $\oint B \cdot dl = \mu_0 (I_c + I_d)$