Image distribution and surface potential of a dipole in a one-shell conducting sphere

An image solution to account for the static electric field on the surface of a one-shell conducting sphere with an internal source, relevant for example to the electroencephalography problem for a spherical model of the human head, is derived and analysed. The image of a point dipole is found to contain a series of point dipoles and a piecewise continuous distribution of dipoles along the line segment between the source point and the centre of the sphere. These image line sources obey simple power and logarithmic laws of the position. As it turns out that the image dipole distribution is similar for a source dipole of any direction, the expression for the image-based surface potential takes a simple and manageable form.