We consider two long resistive straight parallel wires carrying opposite constant currents and
calculate the potential and electric field everywhere in space and the surface charge densities
along the wires. The problem is solved through Laplace’s equation in bi-cylinder coordinates, far
from the battery. We compare these calculations with previous known results that used different
methods. We also calculate the numerical solution for the case in which the battery is present, and
show the equipotentials and surface charges close to the battery.