Discussions of the possibility of a tangential E-field external to a current-carrying conductor must include a voltage source and a return path. Here the problem is reduced to (we believe) the simplest possible geometry. Assume that a circular conducting loop has constant emf per unit length and constant resistance per unit length (finite conductivity), and therefore constant DC current. Assume that the loop has a non-zero conductor diameter and zero net charge. We can also assume that Rloop >> Rconductor. A conceptual model might be, for instance, the limiting case of a loop formed from an arbitrarily large number of arbitrarily small solar cells under constant illumination.
In considering the associated E-field, for any arbitrary reference point on the loop, the maximum voltage differential is across the diameter. This is equally true if the reference point is moved to the other end of the diameter, the difference being that the E-field now points in the opposite direction. This leads to the conclusion that there is no inward-directed (radial) E-field inside the loop, and by similar reasoning nor is there one outside of it. Inside the conductor, there is an E-field parallel to the axis and equal to current times resistance per unit length.
The Attempt at a Solution
The question is whether there is any E-field exterior to the conductor, tangential to the surface, and extending beyond it? Some analyses say yes, but ignore the imputed infinite impedance of a DC E-field (see for instance http://www.dannex.se/theory/3.html and figure 5). If the free-standing tangential E-field is real, it would exert motive force on a test charge, which could be the basis for power transfer to a parallel, independent conductor, e.g. a "DC transformer" sans coupling by magnetic means. This effect is not demonstrated to exist. Even superconducting DC transformers are based on magnetic coupling. Is the purported tangential field nugatory here or have I missed something fundamental?