Ampère's circuital law [SEP] named after
Ampère's circuital law
In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823) relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 paper "" and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.
Maxwell's original circuital law.
The original form of Maxwell's circuital
the magnetostatic approximation, and is 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.
Equation.
Equation Electric currents (along a closed curve/wire).
The Biot–Savart law is used for computing the resultant magnetic field B at position r in 3D-space generated by a flexible current "I" (for example due to a wire). A steady (or stationary) current