Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite Bat plate for three different types of interactions: constant potential. constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere plate geometry. simplifying assumptions used in the original Derjaguin approximation (DA) for sphere sphere interaction are avoided. yielding expressions that are more accurate and applicable over the full range of kappa a. These analytical expressions are significant improvements over the existing equations in the literature that :ire valid only for large kappa a because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.