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Biological cells can be treated as an inhomogeneous particle. In addition to biomaterials, inhomogeneous particles are also important in more traditional colloidal science. By using two energy methods that are based on Legendre polynomials and Green's function, respectively, we investigate the interaction between biological cells or colloidal particles in the presence of an external electric field, in an attempt to investigate the effect of inhomogeneity on crossover frequencies across which the interaction force changes from attraction to repulsion or vice versa. The predictions by the two methods agree with each other very well. It is shown that there exist two kinds of crossover frequencies ¿p, one from attraction to repulsion and the other from repulsion to attraction as external frequencies increase. The first ¿p strongly depends on the degree of inhomogeneity, while the second ¿p does not. This work has relevance to manipulation of biological cells or colloidal particles. [ABSTRACT FROM AUTHOR]