It is shown that the gradient of the scalar function-resistance can be used to determine the electric field intensity, (E) over bar = I del R and the Current density, (J) over right arrow = -sigma I del R in the conductor carrying steady state current. Application of the suggested method is straightforward and does not require heavy calculations such as the Laplace's equation which requires assumptions especially in the case of complicated geometries. The calculations also revealed the source of the surface charge density - obtained from the transversal component of the electric field intensity - on the surface of the conductor formed by the steady state current. Bibl. I I (in English; Summaries in English, Russian and Lithuanian).