The Biot-Savart Law

Shortly after Oersted's discovery in 1819 that a compass needle is deflected by a current-carrying conductor, Jean Baptist Biot and Felix Savart reported that a conductor carrying a steady current exerts a force on a magnet.

From their experimental results, Biot and Savart arrived in an expression that gives the magnetic field at some point in space in terms of the current that produces the field. The Biot-Savart law says that if a wire carries a steady current I, the magnetic field dB at a point P associated with an element of the wire ds has the following properties:

The vector dB is perpendicular both to ds (which is a vector units of length and in the direction of the current) and to the unit vector r directed from the element to P. The magnitude of dB is inversely proportional to r2, where r is the distance from the element to P. The magnitude of dB is proportional to the current and the length ds of the element. The magnitude of dB is proportional to,  Where  is the angle between the vectors ds and r.

The Biot-Savart law can be summarized

Where km is a constant that in SI is exactly 10-7 T.m/A.

This constant is usually written , where  is another constant, called the permeability of free space:

Hence,