The electrophoretic motion of two particles in a uniform electric field is analyzed using bispherical coordinates. Thin electric double layers on the particle surfaces and Stokes flow of the surrounding fluid are assumed. The particles may be of different sizes and zeta potentials, suspended in an unbounded quiescent Newtownian fluid. The particles are separated by an arbitrary distance, and their line of centers has arbitrary orientation with respect to the electric field. Extensive mathematical treatment is performed on the solutions of the electrostatic and hydrodynamic governing equations, which are solved using scalar stream functions, potential functions, and auxiliary functions in series forms. As a result, fast and accurate solutions are possible for very wide ranges of particle separations and size ratios, thereby extending previous work on electrophoretic mobility functions for interacting particles. The new code can be incorporated directly into other codes which require electrophoretic mobility functions. As an example, pairwise electrophoretic heteroaggregation rates are calculated using the new code.