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In physics, specifically electromagnetism, the Biot–Savart law (/ ˈ b iː oʊ s ə ˈ v ɑːr / or / ˈ b j oʊ s ə ˈ v ɑːr /) [1] 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.
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]
Jean-Baptiste Biot (/ ˈ b iː oʊ, ˈ b j oʊ /; [2] French:; 21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who co-discovered the Biot–Savart law of magnetostatics with Félix Savart, established the reality of meteorites, made an early balloon flight, and studied the polarization of light.
Magnetostatics is the study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary.
Alternatively, introductory treatments of magnetism introduce the Biot–Savart law, which describes the magnetic field associated with an electric current. An observer at rest with respect to a system of static, free charges will see no magnetic field.
Biot–Savart law describes the magnetic field set up by a steady current density. Named for Jean-Baptiste Biot and Félix Savart . Birch's law , in geophysics , establishes a linear relation of the compressional wave velocity of rocks and minerals of a constant average atomic weight.
Savart became a professor at Collège de France in 1820 and was the co-originator of the Biot–Savart law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed and published in 1820. [4] The Biot–Savart law relates magnetic fields to the currents which are their sources.
A scientific law is "inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present". [7] The production of a summary description of our environment in the form of such laws is a fundamental aim of science.