What is the relationship between an electric current and a magnetic field called?

The relationship between an electric current and a magnetic field is called electromagnetism. This term encompasses the phenomena by which electric currents produce magnetic fields and how changing magnetic fields can induce electric currents in conductors. Electromagnetism is a fundamental aspect of physics that describes how charged particles interact through electric and magnetic forces, which are interconnected and form the foundation for many modern technologies, including motors, generators, and transformers.

Electrodynamics refers to the study of the behavior of electric charges in motion, particularly the forces they exert on each other, but it doesn't capture the broader relationship with magnetic fields as clearly as electromagnetism does. Electrostatics deals with stationary electric charges and their electric fields, while magnetostatics pertains specifically to stationary magnetic fields created by stationary currents. These related concepts do not fully encompass the dynamic relationship between electric current and magnetic fields inherent in electromagnetism.