Ampere's magnetic circuital law: a simple and rigorous two-step proof

A new proof of Ampere's law from the Biot-Savart law is presented. In the f irst step, a physical interpretation of current as moving charges carrying their electric fields with them simplifies the derivation of the magnetic f ield of current in a straight infinitely long conductor. The m.m.f. of a fi nite electric circuit linking a magnetic path is synthesized from those of two infinitely long wires carrying equal currents in opposite directions, o nly one of them threading the path. This makes the second step rigorous, en abling a non-mathematical treatment of the magnetic effects of electric cur rents in free space.