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Concept
Biot–Savart law
Summary
In physics, specifically electromagnetism, the Biot–Savart law (ˈbiːoʊ_səˈvɑr or ˈbjoʊ_səˈvɑr) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.
The Biot–Savart law is used for computing the resultant magnetic field B at position r in 3D-space generated by a filamentary current I (for example due to a wire). A steady (or stationary) current is a continual flow of charges which does not change with time and the charge neither accumulates nor depletes at any point. The law is a physical example of a line integral, being evaluated over the path C in which the electric currents flow (e.g. the wire). The equation in SI units is
where is a vector along the path whose magnitude is the length of the differential element of the wire in the direction of conventional current. is a point on path . is the full displacement vector from the wire element () at point to the point at which the field is being computed (), and μ0 is the magnetic constant. Alternatively:
where is the unit vector of . The symbols in boldface denote vector quantities.
The integral is usually around a closed curve, since stationary electric currents can only flow around closed paths when they are bounded. However, the law also applies to infinitely long wires (this concept was used in the definition of the SI unit of electric current—the Ampere—until 20 May 2019).
To apply the equation, the point in space where the magnetic field is to be calculated is arbitrarily chosen ().
Official source
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