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Biot-Savart Law

The quantitative expression for magnetic induction (or flux density) was served experimentally by Biot and Savert. Taking the deflection of a compass needle as a measure of the intensity of magnetic field of a current, varying in magnitude and shape, the two scientists concluded that any current element projects into space a magnetic field the magnetic flux density of which, δ B, is directly proportional to the length of the element 9 ) the current I, the sine of the angle θ between he direction of the current and the vector joining a given point of the field and the current element, and is inversely proportional to the square of the distance of the given point from the current elementary

i.e      δB ∝ l sin θ

or       δB = K l sin θ
where K is the proportionality constant which depends upon the magnetic properties of the medium and the system of units employed. In R.M.K.S.S or SI system of units  K = μoμr

where μo is the permeability of free space  in the SI systems and is equal to  4π x 0-7 H/m and μr is the relative permeability of the medium

                                     δB = μoμr   l sin θ
                                              4π      r2

and the field intensity    δB = δB  = l sin θ
                                          μoμr    4πr2

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