The Poisson-Boltzmann equation describing the electrical potential distribution around a charged spheroidal surface in an electrolyte solution is solved analytically under the Debye-Huckel condition. A general boundary value problem is discussed in which an arbitrary combination of potential and charge density is specified at the surface, The method of reflections is proposed for the resolution of the governing Poisson-Boltzmann equation. The conventional constant potential (Dirichlet) problem and constant surface charge (Neumann) problem can be recovered as special cases of the present model. The problem of nonuniformly distributed potential/charges over a surface is also analyzed. A typical example in practice is that the distribution of charges is patchwise. We show that neglecting the nonuniformity of the charged condition over a surface may lead to a significant deviation.