Biot-Savarts Law

The elementary source of magnetic force is a small length dl (or a length element) of a conductor carrying a current I. The force on another similar conductor can be expressed conveniently in terms of a magnetic field dB due to the first. The dependence of such magnetic field on the current I, on the size and orientation of the line element d1, and on the distance r from it was guessed at by Biot and Savart from measurements on finite (not infinitesimal) current-carrying wires with simple shapes, e.g. lines, rectangles and circles. These measurements were of forces as well as come equilibrium near such wires. This direction turns out to be that of the total resultant magnetic field, i.e., the vector sum of the magnetic fields due to the current-carrying wire and the earth.

The magnitude of the magnetic field dB at a distance r from a current element dl carrying a current I is found to be proportional to I, to the length dl and inversely to the square of the distance |r|. The direction of the magnetic field is perpendicular to the line element dl as well as the radius r.

oIdl x r

dB =----- ------- tesla (Wb/m2)

r3