How did James Clerk Maxwell turn Faraday’s experimental ideas into a mathematical theory?

James Clerk Maxwell transformed Michael Faraday’s experimental insights into a rigorous mathematical framework by synthesizing Faraday’s concept of lines of force with his own mechanical models and field theory.12

While Faraday visualized electromagnetic effects through lines of induction and changing magnetic flux, Maxwell provided the quantitative structure to these ideas. In the early 1860s, Maxwell formulated a set of partial differential equations that defined the relationship between electric and magnetic fields and their sources. A critical advancement in this theory was Maxwell’s postulation that changing electric fields also act as sources of magnetic fields, a concept that complemented Faraday’s discovery that changing magnetic fields induce electric fields.13

Maxwell’s work, known as Maxwell’s equations, unified these phenomena into a single theory of electromagnetism. By demonstrating that these fields propagate as waves at the speed of light, he famously identified light itself as an electromagnetic radiation phenomenon.342