Biot-Savart law determines the magnetic field strength produced by an electric current. It was discovered by the French physicists J. B. Biot and F. Savart in 1820 and formulated in general form by the French scientist P. Laplace. According to the Biot-Savart law, a short element of a conductor Δl (Fig.) carrying a current I (the element Δl is assigned the direction of the current I) produces at a point M lying at a distance v from Δl (Δl≤r) a magnetic field of strength ΔH=k(IΔlsin v)/r2 . Here Δl — the angle between Δl and the radius vector r drawn from the element to the point M, and k is a coefficient of proportionality that depends on the choice of the system of units. In the Gaussian system of units k=1/c, and in SI k=1/4π.
The direction of ΔH is given by the right-hand screw rule. The total magnetic field strength H produced at the point M by the current-carrying conductor is equal to the vector sum of the magnetic field strengths ΔH from all the elements Δl of the conductor. In particular, at a distance d from a long (length >= d) straight wire carrying a current, the total magnetic field strength is H=k•2I/d; at the centre of a circular loop of radius R carrying a current H=k•2πI/R, and on its axis at a point lying at a distance d>=R from the plane of the loop H=k•2πR2I/d3; on the axis of a solenoid with n turns per unit length H=k•πnI.
The Biot-Savart law can also be regarded as a law determining the magnetic induction ΔB (in the Gaussian system ΔB=μΔH, in SI ΔB=μμ0ΔH, where μ is the magnetic permeability of the medium, (μ0=4 π•10-7 H/m — the magnetic permeability of vacuum).
The Biot-Savart law can also be regarded as a law determining the magnetic induction ΔB (in the Gaussian system ΔB=μΔH, in SI ΔB=μμ0ΔH, where μ is the magnetic permeability of the medium, (μ0=4 π•10-7 H/m — the magnetic permeability of vacuum).