  An exact solution is given for a two-dimensional model of a Coulomb gas, more
general than the previously solved ones. The system is made of a uniformly
charged background, positive particles, and negative particles, on the surface
of a sphere. At the special value $\Gamma = 2$ of the reduced inverse
temperature, the classical equilibrium statistical mechanics is worked out~:
the correlations and the grand potential are calculated. The thermodynamic
limit is taken, and as it is approached the grand potential exhibits a
finite-size correction of the expected universal form.
