Ampère's circuital law



In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It is the magnetic analogue of Gauss's law, and one of the four Maxwell's equations that form the basis of classical electromagnetism.

Original Ampère's circuital law
In its historically original form, Ampère's Circuital law relates the magnetic field $$\mathbf{B}$$ to its source, the current density $$\mathbf{J}$$. The equation is not in general correct (see "Maxwell's correction" below), but is correct in the special case where the electric field is constant (unchanging) in time.

The law can be written in two forms, the "integral form" and the "differential form". The forms are equivalent, and related by the Kelvin-Stokes theorem.