Biot-Savart Law

Soon after Oersted's discovery, Jean-Baptiste Biot and Felix Savart carried out quantitative experiments (1819) on the force felt by a magnet placed near a current-carrying wire, and from these they derived a mathematical expression -- the Biot-Savart law -- for the magnetic field at any point in space due to the current producing it. Crucially, the law holds for a conductor of any shape, since it is stated for an infinitesimal current element and then summed (integrated) over the whole conductor; §3.8.2 through §3.8.6 apply it to a st …