Identifying the source of electrons producing polar cap arcs (P-C arcs), ubiquitous under northward interplanetary magnetic field (IMF) conditions, should be a notable step toward solving the long-standing problem of determining the topology of the magnetosphere for northward IMF. We calculate several electrodynamics limits that follow from a kinetic theory perspective of electrons precipitating into the polar cap from the electron reservoir in the distant magnetospheric tail, for currents sustainable without electron acceleration. We then calculate mutual relationships between several electrodynamics parameters for currents beyond these limits, if electron acceleration processes were to draw the additional current-carrying electrons from this same reservoir. We compare these theoretical limits and mutual relationships with those actually observed in the polar cap. We conclude that for typical P-C arc conditions, there is no need to look further than the magnetospheric tail for the source reservoir of electrons needed to provide observed fluxes in either polar rain or P-C arcs. We close by putting this into the context of relevant models.