Ampère's fame mainly rests on his establishing the relations between and , and in developing the science of , or, as he called it, . On 11 September 1820 he heard of discovery that a is acted on by a voltaic current. Only a week later, on 18 September, Ampère presented a paper to the Academy containing a much more complete exposition of that and kindred phenomena. On the same day, Ampère also demonstrated before the Academy that parallel wires carrying currents attract or repel each other, depending on whether currents are in the same (attraction) or in opposite directions (repulsion). This laid the foundation of .
The topic of thus begun, Ampère developed a mathematical theory which not only described the electromagnetic phenomena already observed, but also predicted many new ones.
During 1828, he was elected a foreign member of the .