The Biot-Savart’s law the relation between current and the magnetic field it produces. Figure shows a finite conductor XY carrying current I. Consider an infinitesimal element dl of the conductor. The magnetic field ݀vector dB due to this element is to be determined at a point P which is at a distance r from it. Let θ be the angle between dl and the displacement vector r.
According to Biot-Savart’s law, the magnitude of the magnetic field ݀vector dB is proportional to the current I, the element length |݈݀vector dl |, and inversely proportional to the square of the distance r. Its direction is perpendicular to the plane containing ݀vector dl and vector r.
Thus, in vector notation,
where ε0/4π is a constant of proportionality. The above expression holds when the medium is vacuum. The magnitude of this field is,
where we have used the property of cross-product. Equation (1) constitutes our basic equation for the magnetic field. The proportionality constant in SI units has the exact value,
We call µ0 the permeability of free space (or vacuum).
