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The Biot–Savart law [4]: Sec 5-2-1 is used for computing the resultant magnetic flux density 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.
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.
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.
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 = (′) (′) | ′ | ′
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 ...
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.
Magnetic current imaging uses the magnetic fields produced by currents in electronic devices to obtain images of those currents. This is accomplished through the fundamental physics relationship between magnetic fields and current, the Biot-Savart Law:
The magnetic field generated by a steady current I (a constant flow of electric charges, in which charge neither accumulates nor is depleted at any point) [note 8] is described by the Biot–Savart law: [21]: 224 = ^, where the integral sums over the wire length where vector dℓ is the vector line element with direction in the same sense as ...