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Though sufficient for local conservation of charge, Maxwells displacementcurrent is not necessary. An alternative to the Ampere-Maxwell equation isexhibited and the alternatives electric and magnetic fields and scalar andvector potentials are expressed in terms of the charge and current densities.The magnetic field is shown to satisfy the Biot_Savart Law. The electric fieldis shown to be the sum of the gradient of a scalar potential and the timederivative of a vector potential which is different from but just as tractableas the simplest vector potential that yields the Biot_Savart Law Thealternative describes a theory in which action is instantaneous and so mayprovide a good approximation to Maxwells equations where and when the finitespeed of light can be neglected. The result recalls the Darwin approximationwhich arose from the study classical charged point particles to order (v/c)2 inthe Lagrangian. Unlike Darwin, this approach does not depend on theconstitution of the electric current. Instead, this approach grows from astraightforward revision of the Ampere Equation that enforces the localconservation of charge.

How a charge conserving alternative to Maxwells displacement current entails a Darwin like approximation to the solutions of Maxwells equations