The current density near the end of an untwisted multifilament superconducting wire is calculated for a fixed rate of change of transverse applied field. It is shown that the current flow is described by a series of zones with sharp boundaries between them, in analogy with domains in a ferromagnetic material. The zones are characterized by E
z= 0 and

, where E
zis the macroscopic axial electric field. A measurement of the magnetic moment of the wire provides a means for obtaining the transverse conductivity of the conductor.