We solve the problem of a resistive toroid carrying a steady azimuthal current. We use standard toroidal coordinates, in which case Laplace's equation is R-separable. We obtain the electric potential inside and outside the toroid, in two separate cases: 1) the toroid is solid; 2) the toroid is hollow (a toroidal shell). Considering these two cases, there is a difference in the potential inside the hollow and solid toroids. We also present the electric field and the surface charge distribution in the conductor due to this steady current. These surface charges generat not only the electric field that maintains the current flowing, but generate also the electric field outside the conductor. The problem of a toroid is interesting because it is a problem with finite geometry, with the whole system (including the battery) contained within a finite region of space. The problem is solved in an exact analytical form. We compare our theoretical results with an experimental figure demonstrating the existence of the electric field outside the conductor carrying steady current.

In this work we consider a long, resistive cylindrical shell carrying a steady current. A battery in the middle of the wire generates the current. We study the behavior of the potential, electric field and surface charges close to the battery

En este trabajo consideramos una capa resistiva cilíndrica que transporta una corriente constante. Una batería genera la corriente en el centro del conductor. Estudiamos el comportamiento del potencial, campo eléctrico y cargas superficiales cerca de la batería

Apresentamos a primeira tradução para o português do trabalho fundamental de Gauss que é a base do sistema absoluto de medidas eletromagnéticas.

We present the first portuguese translation of the fundamental work by Gauss which is the basis of the absolute system of electromagnetic measures.