We consider the steady motion of space charge from an injecting electrode to an earthed electrode in both a gas and a dielectric. Three models governing the process of charge injection from the electrode into the medium are compared and the resulting voltage-current characteristics calculated. In particular we examine injection laws in which the electric field, charge or current are specified. It is shown that if the injecting electrode is small in comparison to the underlying geometry then the resulting field distribution is almost independent of the injection process. The stability of the three models is compared and it is shown that the field specified and charge specified models are always stable. The calculations are performed exactly for the case of a symmetric problem and make use of the Deutsch approximation for a needle-plane geometry.