We consider the potential magnetic field associated with a helical electric line current flow, idealizing the near-potential coronal field within which a highly localized twisted current structure is embedded. It is found that this field has a significant axial component off the helical magnetic axis where there is no current flow, such that the flux winds around the axis. The helical line current field, in including the effects of flux rope writhe, is therefore more topologically complex than the straight line and ring current fields sometimes used in solar flux rope models. The axial flux in magnetic fields around confined current structures may be affected by the writhe of these current structures such that the field twists preferentially with the same handedness as the writhe. This property of fields around confined current structures with writhe may be relevant to classes of coronal magnetic flux ropes, including structures observed to have sigmoidal forms in soft X-rays and prominence magnetic fields. For example, ``bald patches'' and the associated heating by Parker current sheet dissipation seem likely. Thus, some measurements of flux rope magnetic helicities may derive from external, near-potential fields. The predicted hemispheric preference for positive and negative magnetic helicities is consistent with observational results for prominences and sigmoids and past theoretical results for flux rope internal fields.