The branch of physics that studies electric charges in motion, including their magnetic effects, is electromagnetism.
Electromagnetism unites electricity and magnetism as two aspects of one fundamental interaction. Static charges produce electric fields, while moving charges—such as current in a wire—produce magnetic fields. A changing magnetic field can also induce an electric current, the phenomenon Faraday investigated in the 1830s.
Faraday’s experiments supplied the physical foundation for electromagnetic induction and the field concept. James Clerk Maxwell later expressed these relationships mathematically in Maxwell’s equations during the 1860s. Electromagnetism now encompasses electrostatics, magnetostatics, electrodynamics, electromagnetic waves, and light.
A common mix-up is “electrodynamics,” which more narrowly emphasizes time-varying electric and magnetic fields and moving charges. It is part of the broader subject of electromagnetism, making the stored answer the standard quiz answer.