The method of symbolic operator representation (SOR), which was introduced by Rayleigh [The Theory of Sound, vol. II, 2nd edn., Dover, New York] and applied to colloidal particles by Brenner [Chem. Eng. Sci. 19 (1964) 519], Brenner and Haber [Chem. Eng. Commun. 27 (1984) 283] and Haber and Brenner [Chem. Eng. Commun. 27 (1984) 296], is used to derive an exact solution for the velocity and electric fields of a particle in an infinite medium. The solution is obtained as an infinite series of pertinent vector functions. The first two terms of the solution are identical to a known expression, which was derived by an expansion method. Furthermore, an example is given to demonstrate the usefulness of the method of SOR in solving complex problems of particulate flows.