The theory of continuous media is employed in developing a dynamical theory to explain the interaction of electromagnetic fields with a two-fluid mixture. The fluids are considered charged and electrically conducting, but are not polarized or magnetized. Relativistic and thermal effects are not included. The field equations are postulated in integral form for the entire mixture instead of each fluid separately. This gives fewer conceptual difficulties, especially when electromagnetic variables are present. A brief derivation of the appropriate boundary conditions for a fixed surface of discontinuity and the conservation of energy equation is then given. The general constitutive equations are constructed from a linear series of the various objective velocity variables. The effective electric field is assumed to give each fluid a preferred direction for fluid flow and charge conduction. By the proper reduction of these equations, a mathematical model is obtained which gives a modification of Fick's law of diffusion to account for the effect of an applied electric field. Finally, numerical solutions are presented for the fluid diffusion between two parallel plates maintained at a constant potential difference. The effect of a linear semiconductor slab on one plate with an initial surface charge is also included.