What is Displacement Current? (Maxwell's Discovery)

Ampere's Circuital Law stated that a magnetic field is produced only by moving electrical charges (conduction current in a wire). However, Maxwell noticed a huge problem when looking at a charging Capacitor (two parallel metal plates with an empty gap of air between them).

• Electricity flows through the wire to the plate, but the physical gap between the plates has absolutely zero wire, zero electrons flowing, and zero normal current ($I=0$).
• Yet, a compass placed between the empty gap still deflected, proving a magnetic field existed there! Ampere's law could not explain how a magnetic field was crossing empty space.

Maxwell realized that while there is no physical wire between the capacitor plates, as the plates charge up, the Electric Field (Flux) in that empty space is rapidly increasing (changing over time).

Definition: The current that comes into existence, not because of flowing electrons, but purely because of a rapidly changing electric field (or electric flux) in a region of time and space, is called Displacement Current ($I_d$).

He proved: A changing Electric Field produces a Magnetic Field.

Maxwell corrected Ampere's formula by adding his new displacement current to the normal conduction current ($I_c$).

The new total current = $I_c + I_d$ The formula for displacement current is: $I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$ (Where $\varepsilon_0$ is permittivity, and $d\Phi_E/dt$ is the rate of change of electric flux).