A Remark on Maxwell's Displacement Current

Abstract

One usually derives Ampere's law by taking the curl of the magnetic field given by the law of Biot and Savartfor a volume distribution of currents J. In the derivation, one drops a term that contains ∇ · J, in order to treat stationary processes. It is shown that if that term is kept one gets, for ∇ × H, a term which is the usual conduction current J plus a second term similar to Maxwell's displacement current, present even outside the current distribution J. That extra term is δD0/δt, where D0 = ε0E0 and E0 is the instantaneous Coulomb field produced by the charges in question.