Maxwell was deeply influenced by Faraday's work but he was not his student: he first noticed Faraday’s work while he was at Cambridge in the 1850s. He found a way to translate Faraday’s experimental findings (expressed as the interaction of "lines of force") into a mathematical model (with fields), also taking into account Coulomb's and Ampère's laws. Maxwell then extended that model to take into account the conservation of charge / the continuity of currents.

While Maxwell’s work was inspired by Faraday's, it was also built upon the contributions of many other scientists (Coulomb, Ampère, Thomson, Neumann, Lenz, ...)