How do changing electric fields produce magnetic fields according to Maxwell’s theory?

According to Maxwell’s equations, a changing electric field produces a magnetic field, a concept that serves as a fundamental extension of Ampère’s law.12

James Clerk Maxwell postulated that a magnetic field is associated with a varying electric field even in the absence of a conduction current. To account for this, he introduced the concept of displacement current, which is proportional to the rate of change of the electric field. This theoretical addition ensures the continuity of magnetic effects, such as those observed between the plates of a capacitor where no actual charge flows through the insulation.341

In the modern mathematical formulation of electromagnetism, this relationship is expressed as one of the four Maxwell equations, which states that circulating magnetic fields are produced by both electric currents and changing electric fields. This interaction is essential for the propagation of electromagnetic radiation, as it allows varying electric and magnetic fields to sustain each other as they travel through space as waves.235