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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.
In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay (retarded time) of the fields due to the finite speed of light and relativistic effects.
If all currents in a system are known (i.e., if a complete description of the current density () is available) then the magnetic field can be determined, at a position r, from the currents by the Biot–Savart equation: [3]: 174 = (′) (′) | ′ | ′
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.
Coulomb's law can be found from Gauss's Law (electrostatic form) and the Biot–Savart law can be deduced from Ampere's Law (magnetostatic form). Lenz's law and Faraday's law can be incorporated into the Maxwell–Faraday equation. Nonetheless they are still very effective for simple calculations. Lenz's law; Coulomb's law; Biot–Savart law ...
The force exerted by I on a nearby charge q with velocity v is = (), where B(r) is the magnetic field, which is determined from I by the Biot–Savart law: = ^. The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential.
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.
In the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes equations around an infinitely long cylinder.