The surface charges and the electric field outside steady current carrying conductors has been for long the subject of many investigations. It turns out that both quantities strongly depend on the configuration of the circuit. In this work an attempt to distinguish and clarify the essential factors of this dependence is presented. To this end, a simple, three-dimensional model is proposed and quantitative results are derived which are in agreement with experimental data. In addition, the existence of electric fields outside current carrying conductors and their behaviour can be easily demonstrated in class by recourse to the model, with the help of a computer program, thus avoiding inconvenient or dangerous experimental set-ups
