This paper calculates the electric and magnetic fields and the Poynting vector around two infinitely long parallel cylindrical conductors, carrying a DC current. Also the charges on the surface of the wire are calculated, and their istribution is visualized. The wire is assumed to be perfectly electrically conducting. Furthermore, the Hall effect is ignored. In literature, the problem of determining the electric field is usually tackled using an equivalent model consisting of two line charge densities, producing the same electric field. In this work, the Laplace equation is rigorously solved. The authors found no work explaining the solution of the Laplace equation with boundary conditions for this problem and hence thought it was useful to dedicate a paper to this topic. The method of separation of variables is employed and a bipolar coordinate system is used. After solving the appropriate Sturm-Liouville problems, the scalar potential is obtained. Taking the gradient yields the electric field.
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