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 nqv_dA 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,