Faraday’s breakthrough came when he wrapped two insulated coils of wire around an iron ring

I just realized that I’ve been confusing Faraday and Maxwell. It’s Maxwell who did the 4 equations.

Faraday’s breakthrough came when he wrapped two insulated coils of wire around an iron ring, and found that upon passing a current through one coil a momentary current was induced in the other coil.[2] This phenomenon is now known as mutual induction.[44] The iron ring-coil apparatus is still on display at the Royal Institution. In subsequent experiments, he found that if he moved a magnet through a loop of wire an electric current flowed in that wire. The current also flowed if the loop was moved over a stationary magnet. His demonstrations established that a changing magnetic field produces an electric field; this relation was modelled mathematically by James Clerk Maxwell as Faraday’s law, which subsequently became one of the four Maxwell equations, and which have in turn evolved into the generalization known today as field theory. Faraday would later use the principles he had discovered to construct the electric dynamo, the ancestor of modern power generators and the electric motor.
In 1832, he completed a series of experiments aimed at investigating the fundamental nature of electricity; Faraday used “static”, batteries, and “animal electricity” to produce the phenomena of electrostatic attraction, electrolysis, magnetism, etc. He concluded that, contrary to the scientific opinion of the time, the divisions between the various “kinds” of electricity were illusory. Faraday instead proposed that only a single “electricity” exists, and the changing values of quantity and intensity (current and voltage) would produce different groups of phenomena.[2]
Near the end of his career, Faraday proposed that electromagnetic forces extended into the empty space around the conductor. This idea was rejected by his fellow scientists, and Faraday did not live to see the eventual acceptance of his proposition by the scientific community. Faraday’s concept of lines of flux emanating from charged bodies and magnets provided a way to visualize electric and magnetic fields; that conceptual model was crucial for the successful development of the electromechanical devices that dominated engineering and industry for the remainder of the 19th century.