By the time James Clerk Maxwell began his research in a related subject in the 1850s, Ampere's law, which connects a constant electric current to a rotating magnetic field, was well established. Ampere's law was recognized to only be applicable in static circumstances, which involved stable currents.
The extension of the applicability of Ampere's law to time-dependent circumstances of this law was made possible by Maxwell's effort to have additional of another source term, a change of electric flux. More importantly, Maxwell was able to differentiate the electromagnetic character of light and create a whole theory of electromagnetism thanks to the inclusion of this part in the Ampere's equation, now known as the Ampere-Maxwell's law.