The idea that a cluster of droplets evaporates in times longer than a single droplet and that the droplets near the edge of the cluster evaporate most rapidly is based on observational evidence. In this work, we use a theoretical model based on the electrostatic-image-charge method to calculate the vapour density field for a cloud of monodisperse cloud droplet size distribution immersed in an undersaturated environment. Calculations are performed for variations of droplet size, droplet number, droplet separation, relative humidity and temperature of the environment. The results show the screening effect produced by the outermost droplets of the cluster, which reduces the effect of the vapour density at infinity within the cluster. Additionally, this model allows us to observe that each droplet within the cluster evaporates with a different evaporation rate according to the position that it occupies within the cluster. Droplets near the edge of the cluster are shown to evaporate faster than droplets within the cluster. The treatment uses a highly simplified description of a droplet cluster, but it nevertheless allows us to build a good theoretical understanding of the microphysical properties of the evaporation process in real cloud systems.