Being given pointwise measurements of the electric potential taken by electrodes on part of the scalp, the EEG (electroencephalography) inverse problem consists in estimating current sources within the brain that account for this activity. A model for the behaviour of the potential rests on Maxwell equation in the quasi-static case, under the form of a Poisson-Laplace equation. We describe our approach for solving the inverse problem in spherical geometry, for piecewise constant electric conductivity values, and pointwise dipolar source terms.