The use of dielectrophoresis is fast becoming a proven technique for manipulating particles and macromolecules in microfluidic systems. Here an analytic solution for the gradient in the electric field strength, delta (E . E) [corrected] produced by a two-dimensional array of parallel electodes is derived using the method of Green's functions. The boundary condition for the potential between electrodes is estimated by using a linear approximation. While the Green's function used here is somewhat different from Wang et al., J. Phys. D 29, 1649 (1996), the resulting analytic expression for the potential field is in exact agreement with their result. Selected results for equispaced electrodes with equal widths are compared with Wang et al., J. Phys. D 29, 1649 (1996). The analytic solution is employed to study the effects of electrode spacing and electrode width on the gradient in electric field intensity. Results show that the magnitude in the gradient in the electric field intensity exhibited the expected dependence on the applied voltage; however, the dependence on electrode width was found to be on the order of the electrode width squared. Results to explore the effects of electrode spacing show that as the spacing is reduced below two electrode widths the magnitude of the gradient increases exponentially.