DISPLACEMENT CURRENT
Maxwell expanded upon Ampère's circuital law to include a new type of current, termed displacement current, which arises from changing electric fields. This addition was crucial for resolving inconsistencies observed in the traditional application of Ampère's law in scenarios involving capacitors, particularly when dealing with changing electric fields.
When charging a parallel plate capacitor, the electric field between the plates varies with time, which in turn influences the surrounding magnetic field. The displacement current, defined as
$$
i_d = rac{ε_0}{dt} rac{dΦ_E}{dt}
$$
acts in a similar manner to conduction current. Here, $Φ_E$ represents the electric flux through the surface bounded by a closed loop that surrounds the capacitor's plates.
Maxwell's generalization of the Ampère's law can then be expressed as the sum of conduction and displacement currents, demonstrating that a changing electric field can produce a magnetic field, effectively supporting the existence of electromagnetic waves. These waves propagate through space at the speed of light, revealing the interconnected nature of electricity, magnetism, and light.
This discovery was pivotal, as it not only unified the laws governing electricity and magnetism but also paved the way for understanding the generation and propagation of electromagnetic waves, which manifest in various forms such as radio waves and visible light.