Biot Savart Law : Definition, Formula

Biot Savart Law : Definition, Formula

The Biot-Savart Law is a fundamental law in electromagnetism that describes how electric currents produce magnetic fields. It states that the magnetic field produced at a point in space by a steady current is proportional to the current, the length of the current-carrying segment, and the sine of the angle between the segment and the point, and inversely proportional to the square of the distance from the point to the segment. 

In 1820, Biot and Sievert did many experiments to study the magnetic field generated by current carrying conductors. On the basis of these experiments, he told that the value of the field ∆B at a point P in the magnetic field produced by a fraction of a current-carrying conductor ∆l depends on the following factors-

(i) The magnetic field ∆B is directly proportional to the current i flowing in the conductor.

    ie.      ∆B ∝ i

(ii) The magnetic field is directly proportional to the length l of the segment of the conductor.

     ie.      ∆B ∝ ∆l

(ii) The magnetic field is directly proportional to the length of the segment and the sine of the angle formed by the line joining the segment to that point P.

    ie.       ∆B ∝  sinθ 

(iv) The magnetic field is inversely proportional to the square of the distance r from the point P.

    ie.       ∆B ∝ 1/r²

Putting the above four facts together

                ∆B ∝ i∆l / sinθ / r²

This relation is called Biot-Savart's law.

If the conductor is located in vacuum (or air), then this relation is written in the form of the following formula.

        ∆B = μ0/4π (i∆l /sin /r²)

where μ0/4π is the constant of proportionality. μ0 is called the permeability of vacuum. If i is in ampere and ∆l and r are in meter, then its value is 4π ✖ 10-⁷ Newton/ampere². The dimension of μ0 is [MLT-² A-²].

The direction of the magnetic field generated by the current carrying conductor is determined by right hand palm rule number 1 or Maxwell's clockwise screw rule.

In the figure above, the sign X indicates the direction of the magnetic field perpendicular to the plane of the paper downwards and the sign ⚈ indicates the direction of the magnetic field perpendicular to the plane of the paper upward.