André-Marie Ampère

Direction determines attraction or repulsion.

Place two long parallel wires near one another. Each wire creates a magnetic field that acts on the current in the other wire. When conventional currents run in the same direction, the wires attract. When the currents run in opposite directions, the wires repel.

This direction rule is sometimes stated incorrectly. The correct physical result is same direction → attraction and opposite direction → repulsion.

Ampère generalized the result mathematically.

Ampère related the mutual action of current-carrying wire elements to current intensity and geometry. The modern circuital law connects the circulation of magnetic field around a closed path to the current enclosed by that path, with Maxwell later extending it to include changing electric fields.

Many loops reinforce one another.

Ampère also developed the solenoid: wire wound into a long coil. Fields from neighbouring turns combine, producing a relatively strong and nearly uniform field inside a long coil. Add an iron core and the device becomes a practical electromagnet—the principle used in relays, valves, actuators and contactors.