Ampère's Circuital Law

A law relating the circulation (line integral) of the magnetic field around a closed loop to the total conduction current and the displacement current passing through any surface bounded by that loop; in Maxwell's extension it includes the displacement current term.

In classical electromagnetism, the line integral of the magnetic field B around any closed curve C equals the permeability of free space μ0 times the net conduction current I_enc passing through any surface S bounded by C, extended in Maxwell–Ampère form by adding the displacement current term μ0ε0 d/dt of the electric flux through S: ∮_C B·dl = μ0 I_enc + μ0ε0 d/dt ∫_S E·dA.