29.2: Biot-Savart Law
The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two scientists, Jean-Baptiste Biot and Félix Savart, who investigated the interaction between a straight, current-carrying wire and a permanent magnet.
A current-carrying wire creates a magnetic field in its vicinity. Consider an infinitesimal current element dl in a wire. The direction of vector dl is along the direction of the current. The total magnetic field at point P due to all the charges in the current element is the vector sum of the field due to the individual charges. If A is the cross-sectional area, then Adl is the volume of the current element. Considering there are n number of charges per unit volume, nAqdl gives the total charge in the current element, while nqvdA is the current flowing through the wire. Substituting these, the magnitude of the magnetic field can be written in terms of the current as,
Defining a unit vector pointing from dl to P, the magnetic field due to the current element is given by the Biot-Savart law.
The magnetic field due to a finite length of current-carrying wire is found by integrating Equation 2 along the wire,
