An Alternative Introduction to Maxwell's Displacement Current

In introductory texts Ampere's law is generally introduced in the steady-current form $∮B·dℓ=μ0I$⁠, and it is later extended to a more general form^1–4 involving the socalled displacement current $Id$⁠, Here the line integral is to be taken along a closed Amperian loop, and I is the net conventional current that penetrates any surface bounded by the loop. In its steady-current form (without $Id$⁠), Ampere's law is used to find the magnetic field generated by highly symmetric arrangements of current-carrying wires, for example, an infinite straight line of current or an infinite solenoid, in analogy with Gauss's law.