We present a method based on the inversion transformation for obtaining the quasi-static potential
created by an oscillating dipole in the vicinity of two dielectric nanospheres (dimer). In the inversion space, a Poisson equation for another potential
must be solved in which the source is an effective charge density composed of a point dipole and a point charge; the charge of this point charge depends on the radial component of the dipole moment with respect to the inversion center. We particularly derive the solution of the potential
when the dipole is on the dimer axis. Our formalism can provide an alternative physical insight for explaining the radiative properties of localized emitters (molecules) as well as intermolecular interactions mediated by electromagnetic fields. In addition, this method can yield to a less computational effort for calculating the electric field. To illustrate our method, the spatial distributions of the electric field created by a dipole for two particular setups are obtained.