Complete calculation of the electric potential produced by a pair of current source and sink energizing a circular finite-length cylinder

Abstract

Green’s function for the solution of Poisson’s equation in cylindrical coordinates is calculated using the underlying Sturm–Liouville problem. The potential distribution produced by an arbitrarily oriented eccentric dipole located in a homogeneous conducting circular finite-length cylinder is given; three alternative forms are presented, which enable us to compute the potential everywhere in the cylinder. Previous works devoted to this subject were incomplete in the sense that the formulas which were presented there do not converge everywhere. For our expressions of the Green function,we show that Gabor and Nelson’s theorem applies for the present geometry. We also consider the case where the current source and sink are remote from each other in order to check the consistency between Gabor and Nelson’s theorem and Helmholtz’s principle. Applications of our formulas are presented in a situation which is representative of the human trunk activated by the heart and discussion of the results is made in relation with electrocardiology. It is shown that the eccentricity of the dipole is responsible for curving the line of the greatest potentials and for wrapping the zero equipotential plane.