Ampère's law

Ampère's law is the magnetic mirror image of Faraday's law: it says an electric current wraps a magnetic field around itself, like water curling around a stick stuck in a stream. Run a current up a straight wire and the magnetic field circles it in tidy rings, getting weaker the farther out you go. Add up the field as you walk one full loop around the wire and you get a number proportional to the current you enclosed — that's the law in a sentence. Coil the wire and every turn's field stacks up, which is how you build a strong electromagnet from a humble battery.

Maxwell found the original law was incomplete and added the crucial finishing touch: a changing electric field also makes a magnetic field, exactly as if it were a current (he called it 'displacement current'). This wasn't a footnote — it's the piece that lets fields keep regenerating each other and go racing off as light. Without Maxwell's addition the magnetic field around a charging capacitor would have nowhere to come from, since no actual current crosses the gap between the plates.