Simplified analytical analysis of ionized fields associated with HVDC transmission lines is possible if it is based on Deutsch's assumption. The resulting voltagecurrent (V-I) characteristic may be conveniently used to calculate the power losses of a HVDC transmission line. However, such an approach has been criticized because Deutsch's assumption is considered invalid for the line-plane geometry. This paper verifies the validity of the V-I characteristic thus obtained by comparing it with numerical results which are generated using a new method developed by the authors, in which Deutsch's assumption is not employed.using Deutsch's assumption. Some authors [3,4] have argued that Deutsch's assumption is not valid for a lineplane geometry even in the absence of wind. Their studies show that the flux lines of an ionized field do deviate from those of the corresponding charge-free field.Since an analytical expression of the V-I characteristic is a convenient form to use in the design of a HVDC transmission line, it is of practical importance to verify the validity of Deutsch's assumption in the absence of wind. In this paper, results generated by using a new numerical method, developed by the authors [5,6,7], are compared with those obtained by employing the analytical method in [2]. The numerical method does not resort to Deutsch's assumption.