The response of the global and local reactivity density-based descriptors (chemical potential, hardness, softness, Fukui function, and local softness) in the presence of external electric field has been studied for some of the simple prototype molecular systems. In addition to the analysis on the reactivity of these systems, the influence of the electric field on the interaction energy of the complexes formed by these systems has also been studied using the recently proposed semiquantitative model based on the local hard-soft acid-base principle. By using the inverse relationship between the global hardness and softness parameters, a simple relationship is obtained for the variation of hardness in terms of the Fukui function under the external electric field. It is shown that the increase in the hardness values for a particular system in the presence of external field does not necessarily imply that the reactivity of the system would be deactivated or vice versa.