How did James Clerk Maxwell unite electricity and magnetism in one theory?

James Clerk Maxwell united electricity and magnetism by synthesizing existing experimental laws into a consistent mathematical framework known as Maxwell’s equations. Building upon the work of Michael Faraday, Maxwell recognized that electric and magnetic fields are fundamentally interrelated.123

To achieve this unification, Maxwell made a critical theoretical adjustment to Ampère’s law. He introduced the concept of "displacement current", which posited that a changing electric field produces a magnetic field, even in the absence of a conduction current. This addition ensured the logical consistency of his equations regarding the conservation of charge.452

When Maxwell combined these equations, he derived a wave equation describing the propagation of transverse electromagnetic disturbances. He calculated the velocity of these waves using electrical measurements and found it matched the speed of light. This led to the profound conclusion that light itself is an electromagnetic phenomenon, effectively unifying the fields of electricity, magnetism, and optics into one grand design.467