The Electric Field of an Eccentric Dipole in a Homogeneous Spherical Conducting Medium

Abstract

The electrical position of the heart with reference to the electrodes used in studying its field is unknown. For reasons presented, it is more likely eccentric; hence, the equation defining the field of an eccentric dipole in a spherical medium might be useful for projected experimental studies and for better understanding of the way in which a given electrical position determines the electrode potentials. A method introduced by Helmholtz was used for deriving the desired equation. It is discussed since its concepts are of considerable importance to other electrocardiographic problems, too. The more simple mathematical example dealing with the centric dipole in the sphere is discussed. The equation for the field of the eccentric dipole is given and data based upon it are presented in numerical and map form. The Helmholtz equation for the field in the spherical conductor produced by two small spherical electrodes arbitrarily located is also presented and briefly discussed.